A soft morphing ray propulsor capable of generating an undulating motion in its pectoral fins was designed and fabricated. The propulsor used shape memory alloy for actuation, and the body was made with soft polymers. To determine the effects of undulation in the fins, two models that differed in terms of the presence of undulation were fabricated using different polymer materials. The experimental models were tested with a dynamometer to measure and compare thrust tendencies. Thrust measurements were conducted with various fin beat frequencies. Using the experimental data, the concept of an optimized standalone version of the ray robot was suggested and its prototype was fabricated. The fabricated robot was able to swim as fast as 0.26 body length per second and 38% more efficient than other smart material-based ray-like underwater robots.