Mo and V are irreplaceable alloying agents in tailoring microstructures and enhancing mechanical and electrochemical properties of dual-phase steels, high entropy alloys, and ultrahigh-strength steels. Recent experiments have confirmed the miscibility gap in isothermally treated Mo-V binary systems below certain temperatures and identified spinodal decomposition and nucleation growth as two possible phase decomposition mechanisms. The present paper studies the decomposition behavior of Mo-V binary alloys at temperatures in the miscibility gap region using CALPHAD modeling, first-principles calculations, and phase-field simulations. We extend experimental considerations and incorporate the role of cooling rates, compositionally-generated elastic stresses, and applied tractions on the decomposition kinetics in the Mo-V binary alloy system. The phase-field simulations are performed for temperatures within the miscibility gap, various cooling rates, and several loading conditions. We consider periodic structures with cubic symmetry. The effect of temperature, cooling rates, inhomogeneous elasticity, and applied tractions on phase separation kinetics are shown.