Recently, there has been significant interest in developing underwater vehicles inspired by jellyfish. One of these notable efforts includes the artificial Aurelia aurita (Robojelly). The artificial A. aurita is able to swim with similar proficiency to the A. aurita species of jellyfish even though its deformation profile does not completely match the natural animal. In order to overcome this problem, we provide a systematic finite element model (FEM) to simulate the transient behavior of the artificial A. aurita vehicle utilizing bio-inspired shape memory alloy composite (BISMAC) actuators. The finite element simulation model accurately captures the hyperelastic behavior of EcoFlex (Shore hardness-0010) room temperature vulcanizing silicone by invoking a three-parameter Mooney-Rivlin model. Furthermore, the FEM incorporates experimental temperature transformation curves of shape memory alloy wires by introducing negative thermal coefficient of expansion and considers the effect of gravity and fluid buoyancy forces to accurately predict the transient deformation of the vehicle. The actual power cycle used to drive artificial A. aurita vehicle was used in the model. The overall profile error between FEM and the vehicle profile is mainly due to the difference in initial relaxed profiles.