Magnetorheological elastomers are one of the promising options for stiffness variation of soft robots due to their field-dependent behavior producing high stiffness change rapidly. In this study, we have developed a multiphysics finite element model to investigate this unique behavior with a possible application in soft robotics. Sample magnetorheological elastomers were produced, and an experimental setup was developed. Cantilever bending experiments were performed under varying external magnetic field to tune the model. Results show that the elastic modulus increases with increasing external magnetic field as well as dependency on the volume fraction. Additionally, a possible implementation of magnetorheological elastomers as a stiffening module for a soft continuum robot is discussed as well.