Stress can be applied to modulate solid–solid phase transitions because the stress changes the transition energy barrier which determines the phase transition rate. The lower the barrier, the higher the rate and more likely the phase transition occurs. This paper presents a new theoretical method – finite deformation Bell theory (FD-BT), which is developed based on the concept of the original Bell theory, for predicting transition barriers as a function of the applied stress field. The theory is applied to study the phase transitions of two model materials which exhibit distinct transition mechanisms: 2D MoTe2 from 2H phase to 1T′ phase, and silicon from diamond phase to β-tin phase. The theoretical predictions are compared with the atomistic simulation results obtained from the finite deformation nudged elastic band (FD-NEB) method, which has been recently developed to compute stress dependent barriers of the transitions under finite deformation.