Monofins provide swimmers with an efficient alternative to the standard pair of fins. For example, all short and long distance human swimming records have been established using monofins. Current monofin design is mostly empirical, so the objectives of this work are to analyze monofin propulsion through coupled fluid-structure simulation and to optimize its flexural stiffness distribution. The optimization process maximizes the propulsive power provided by the monofin with a constraint on the total expended power. In order to be able to carry out the optimization of the coupled fluid-structure system which is numerically costly to evaluate, the following simplifications are proposed: (i) a twodimensional unsteady, inviscid and incompressible fluid flow is considered; (ii) the swimmer is composed of linear articulated segments, whose kinematics is imposed and identified from experimental data; (iii) the monofin is represented by rigid bars linked by torsional springs. For various allowable swimmer powers optimal 2D stiffness distributions are obtained using the Globalized and Bounded Nelder-Mead algorithm. Finally, an identification procedure is described to translate the optimal 2D stiffness distributions into 3D thickness profiles for a given monofin planform shape.