Acoustic emission (AE) technique, which uses the occurrence of AE phenomena, is a powerful monitoring tool that finds tremendous applications in engineering. Owing to the issues related to characterization of the acquired AE signals, AE technique requires thorough and robust designing, prototyping and testing before being applied for monitoring purposes. The testing of AE technique is often performed using physical experiments. However, these physical experiments - apart from being expensive and time consuming - impose challenges related to repeatability and feasibility of including different types of realistic (buried) AE source(s). Then, using numerical modeling of AE phenomena to perform cheaper and faster repeatable numerical experiments becomes an attractive option to overcome the challenges of physical experiments. Computationally efficient numerical modeling of AE phenomena, however, requires a mutiscale modeling approach. Owing to the employment of different space scales (i.e. spatial grid sizes), multiscale models are often affected by numerical phenomena that affect the results. This thesis is dedicated to the development and analysis of multiscale numerical modeling of AE phenomena. In this thesis, a thorough investigation of the influences of numerical effects on multiscale modeling of AE is performed. The work presented here is a part of the dynamic virtualization (DyVirt) project, and is based on the verification aspect of the V&V (verification and validation) procedure - required for building reliable trusted virtual models. In this thesis, a multiscale coupling scheme capable of dynamically coupling any continuum models of elastic wave propagation - with possibly varying material properties and spatial discretization parameters - is reported. This coupling scheme is employed to couple two appealing local computational strategies for modeling elastic wave propagation, namely, local interaction simulation approach (LISA) and cellular automata for elastodynamics (CAFE). Owing to the advantages of individual LISA and CAFE models, such a LISA-CAFE multiscale model is considered an attractive prospect for very efficient multiscale modeling of AE phenomena. The multiscale LISA-CAFE model was thoroughly analyzed for stability and artificial reflection and transmission properties using analytical approaches. Furthermore, different types of AE source models, which provide excitation to the multiscale model, were developed, and the different numerical phenomena affecting AE source models were thoroughly analyzed using analytical approaches. The stability analysis reported in this thesis was performed in the complex domain of β parameter wherein two vectors rotate in opposite directions. The stability space was represented as a circle, and the critical combinations of the rotating vectors define the stability of the coupled model. Model configurations of practical interest were investigated, and analytical formulas that can predict the stability limit were derived and used to analyze the stability of the LISA-CAFE multiscale model. All the derived analytical formulas were numerically validated with numerical simulations' results, and a complete agreement was observed. The analysis of artificial reflection and transmission reported here is based on the concept of numerical impedance mismatch between the coupled domains. Unlike classical mechanical impedance, numerical impedance is a function of spatial discretization parameters, and in this thesis, the numerical impedances of LISA and CAFE were derived. These numerical impedances were used to develop analytical formulas capable of predicting reflection - both physical and artificial - and transmission for any configuration of LISA-CAFE multiscale model. Moreover, to minimize the amount of artificial reflections, three different analytical strategies are presented in terms of compensation schemes. All the developed formulas and compensation schemes were numerically validated with the results from numerical simulations, and a complete agreement was observed. The spatial grid possesses numerical dispersion and filtering properties that affect the results of AE source models. In this thesis, the influences of spatial grid induced numerical dispersion were analyzed using two different analytical source models based on explicit source-time functions. The influences of filtering properties of the spatial grid, on the other hand, were analyzed using an AE source modeled with cohesive zone approach. Additionally, the influence of the excitation type on AE source models was analyzed. The analyses of stability and artificial reflection and transmission reported in this thesis are general and can be applied to any multiscale model/numerical technique - provided the formulating equations are available. Similarly, the analysis on AE source modeling presented here can be employed to any narrowband or broadband source models. Altogether, this thesis paves the path for the development of trusted virtual models for dynamic-transient phenomena.