Strained semiconductor thin films grown epitaxially on semiconductor substrates of different composition, such as Si1-xGex/Si, are becoming increasingly important in modern microelectronic technologies. In this paper, we report a hierarchical computational approach for analysis of dislocation formation, glide motion, multiplication, and annihilation in Si1-xGex epitaxial thin films on Si substrates. Specifically, a condition is developed for determining the critical film thickness with respect to misfit dislocation generation as a function of overall film composition, film compositional grading, and (compliant) substrate thickness. In addition, the kinetics of strain relaxation in the epitaxial film during growth or thermal annealing (including post-implantation annealing) is analyzed using a properly parameterized dislocation mean-field theoretical model, which describes plastic deformation dynamics due to threading dislocation propagation. The theoretical results for Si1-xGex epitaxial thin films grown on Si (100) substrates are compared with experimental measurements and are used to discuss film growth and thermal processing protocols toward optimizing the mechanical response of the epitaxial film.