Most fish swim with body undulations that result from fluid–structure interactions between the fish’s internal tissues and the surrounding water. Gaining insight into these complex fluid–structure interactions is essential to understand how fish swim. To this end, we developed a dedicated experimental–numerical inverse dynamics approach to calculate the lateral bending moment distributions for a large-amplitude undulatory swimmer that moves freely in three-dimensional space. We combined automated motion tracking from multiple synchronised high-speed video sequences, computation of fluid dynamic stresses on the swimmer’s body from computational fluid dynamics, and bending moment calculations using these stresses as input for a novel beam model of the body. The bending moment, which represent the system’s net actuation, varies over time and along the fish’s central axis due to muscle actions, passive tissues, inertia, and fluid dynamics. Our three-dimensional analysis of 113 swimming events of zebrafish larvae ranging in age from 3 to 12 days after fertilisation shows that these bending moment patterns are not only relatively simple but also strikingly similar throughout early development and from fast starts to periodic swimming. This suggests that fish larvae may produce and adjust swimming movements relatively simply, yet effectively, while restructuring their neuromuscular control system throughout their rapid development.