We will give an overview of a few swimming problems with biological
applications. First, we present a model of fish fin mechanics and solve a simple optimization problem for fish fins: what distributions of elastic
components maximize the stiffness of the fin? We then discuss the
resonant properties of flexible beams in fluid flows, as models for
fish fins and bodies during swimming. Finally, we will discuss a simple model of krill swimming which asks: how should the krill coordinate the motions of its appendages for fast and efficient swimming?