Abstract: Shape memory alloys inherit their macroscopic properties from their mesoscale microstructure originated from the martensitic phase transformation. In a cubic to orthorhombic transition, a single variant of martensite can have a compatible (exact) interface with the austenite for some special lattice parameters in contrast to conventional austenite/twinned martensite interface with a transition layer. Experimentally, the phase compatibility results in a dramatic drop in thermal hysteresis and gives rise to very stable functional properties over cycling. Here, we investigate the microstructures observed in Ti50Ni50-xPdx alloys that undergo a cubic to orthorhombic martensitic transformation using a three-dimensional phase field approach. We will show that the simulation results are in very good agreement with transmission electron microscopy observations. However, the understanding of the drop in thermal hysteresis requires the coupling of phase transformation with plastic activity. We will discuss this point within the framework of thermoelasticity, which is a generic feature of the martensitic transformation. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4712629]