Solid-state batteries (SSBs) show a promise to boost energy density, power density and thermal safety of lithium-ion batteries. Even though solid electrolytes (SEs), owing to their mechanical rigidity, have enabled the use of Li-metal anodes, growth of filaments within the SE still remains a major challenge. Internal stresses and molar volumes of interacting species strongly influence both reaction kinetics at the anode-SE interface and ionic transport within the SE and thus, play an important role in dictating the stability of the solid-solid interfaces during electrodeposition. In this work, we examine the role of mechanics in altering the underlying reaction and transport processes by analyzing various electrochemical and mechanical parameters involved such as molar volumes, shear moduli, applied current density and ionic conductivity. We present a non-dimensional formulation to demarcate regimes of stable/unstable growth. The effects of interface morphology and molar volume variation at the interface have also been studied.