In the present paper, the effect of phase-dependent elastic properties on martensitic phase transformations (PTs) in a single crystal is investigated using the phase field approach. The simplest phase dependence of elastic properties is defined by different Young's moduli for austenite (A) and martensite (M), and its effect is investigated for thermal- and stress-induced propagation of an A-M interface. The phase dependence of elastic properties is then included using the quadratic elastic energy with two constants different for A and martensitic variants. The coupled system of phase field and elasticity equations is solved using the nonlinear finite element method, and various examples of PTs are studied. A planar A-M interface propagation is studied under different thermal and mechanical loadings. It is revealed that the effect of phase-dependent elastic properties is more pronounced when thermal strain is included due to the interplay of elastic, transformational and thermal strains. The thermal-induced growth of a martensitic nucleus and the effect of periodic boundary conditions on the nucleus growth are investigated for both phase-independent (PI) and phase-dependent (PD) elastic properties with thermal strain and without it. Martensitic PTs with two variants are studied under different loadings using a one-fourth model and symmetric boundary conditions to reduce the effect of stress concentrations. Martensitic PTs with two variants are also studied in the presence of two circular holes for both the PI and PD elastic properties. This pronounces the significant effect of heterogeneous stress concentration and the size on the PTs. The effect of phase-dependent elastic properties is also studied on twinning in a martensitic grain embedded inside an austenitic matrix under overcooling. The obtained results reveal a significant effect of phase-dependent elastic properties on different types of martensitic PTs and remarkably change the interpretation of structural transformations at the nanoscale.