Multicellular development depends in large part on the growth, patterning and morphogenesis of epithelial sheets. How individual epithelial cells coordinate tissue-scale processes is still poorly understood due to the inherent complexity of emergent systems-level behavior. Testing hypothetical novel biophysical mechanisms across spatial scales requires computational models that can span subcellular to tissue levels. However, the task of including detailed descriptions of interactions between the cytoplasm, cortically enriched cytoskeleton and intercellular adhesion is challenging due to the prohibitively high computational costs. Here, we introduce a multi-scale modeling environment called Epi-Scale for simulating epithelial tissue dynamics based on the Subcellular Element (SCE) modeling approach. Epi-Scale explicitly simulates the separate mechanical contributions of multiple cellular components. Computational implementation of the model is based on an efficient parallelization algorithm that utilizes clusters of Graphical Processing Units (GPUs) for simulating large numbers of cells within a reasonable computational time. Epi-Scale naturally recapitulates cellular and tissue-scale properties consistent with experimental data. As a demonstration of the predictive power of the model, detailed simulations of increased cell-cell rearrangements as a function of tissue growth rates are described. A particular advantage for the Epi-Scale environment is its extensibility toward investigating complex biological processes of multiple cell types and interactions between cells and extracellular matrix.