— The objective of this article is to make a geometric and numerical analysis about the optimal displacements of a larval copepod swimming at low Reynolds number. A simplified model of locomotion is analyzed in the framework of Sub-Riemannian geometry. In particular, the role of both normal and abnormal geodesics is related to observed geometric motions in relation with the mechanical power dissipated by the swimmer. Numerical simulations of the normal strokes illustrate the computations and the optimal strategy is presented.