We propose the application of a numerical model based on the Method of Fundamental Solutions to the estimation of the target strength (TS) of single fish, a crucial parameter for evaluating fish abundance when using active acoustical techniques. We consider a realistic beam and the influence of the evolution of the scattered field with distance maintaining the target in the far field of the ultrasonic transducer. The cases of a fluid sphere and a prolate spheroid model for the swimbladder are used to verify the application of MFS against other analytical and numerical methods. Additionally, a model considering only the swimbladder and the fishbone is presented to evaluate the differences between dorsal and ventral aspect measurements, and to understand previous experimental works performed with Atlantic salmon (Salmo salar) in floating cages.