A phase-field approach is presented to simulate the evolution of a BCC precipitate in an FCC matrix for AlxCrFeNi based medium entropy systems. The CALPHAD composition dependence of the Gibbs energies and diffusion mobilities for this quaternary alloy are introduced in the model using ThermoCalc with TCHEA2 and MOBNI4 databases. Heterogeneous elastic properties are assumed for the FCC and BCC phase computed for the quaternary system. The effect of the elastic stresses due to lattice mismatch on precipitate shape, evolution and matrix composition is presented for a single BCC precipitate in and FCC matrix. We find that the elastic effects are considerable.