Soft robotic actuators may provide the means to develop a soft robotic catheter, enabling safer and more effective transcatheter procedures. In many clinical applications, device contact force affects the quality of diagnostic or the degree of therapy delivered. Therefore precise end effector force control will be a requirement for the soft robotic catheter. In this study a bending soft actuator system was fabricated, and the relationship between volume input and end effector contact force is examined. Static and dynamic system identification were conducted under two different loading conditions loosely related to actuation in a blood vessel. The experimental data from these tests led to the creation of a non-linear system model. A reduced term model was developed using a Root Mean Square Error (RMSE) method in order to observe the importance of system dynamics and nonlinearities. A different system model was designed for each loading condition. These two reduced models matched with experimental result, but differed in model terms and parameters, suggesting that either loading condition identification or end effector closed-loop sensing will be needed for accurate contact force control of a soft robotic actuator in an intravascular environment.