Abstarct: The internal channel networks embedded within a soft Euler-Bernoulli beam is assumed a soft fluidic actuation. In the soft robotics, it is essential to pay attention to the computation time and accuracy in the modeling toward the control implementation. Hence this thesis optimize an analytical method without any extra computation time when errors decrease, more than 9 percent, at the first. Second, we present the optimal cross-section in the soft fluidic actuations (SFA). Further, for prevention of modeling and analysis different SFAs, we introduced correction functions that capable predict similar SFA behavior by difference channels number and cross-sections. So this functions can have impressive effect on computation time and eliminate need to construction different SFAs in the lab. Afterward we implement designed SFA as a fish tail because it allows our model to swims out of the plane just by one actuation. In this biomimetic design, pressure distribution in the fluid channels creates a bending moment in the tail and it provides thrust force for the fish-like robot. Traditional fish robots swim just in the plane with their tail oscillating, or they have fins on their sides for height change. By adding fins for the out-of-plane motion, dynamic equations will be complex because analysis of fins and tail effects on dynamic behavior simultaneously. In this design, we added two nozzles aligned with the robot's center of mass for swimming out of the plane. The top nozzle moves the body down and conversely. Then we analysis dynamic behavior of fish robot with soft fluidic actuation as a tail in three-dimensional path, for the first time. Proposed mechanism for height change prevents the complex dynamic equations and has noticeable effect on the computation time, on one hand. On the other hand, by implementing the optimal cross-section for the SFA, robot achieves to the least mass and length that improves its maneuverability. Finally, we investigated the power source and fluid energy level in our model for indicating its sufficiency in this applicant.