Metachronal swimming is a locomotion strategy used by freely-swimming crustaceans such as krill. Krill and other crustaceans that use metachronal swimming paddle their swimming legs at Reynolds numbers ranging from approximately 10¹ to 10⁴ dependent on body size and swimming behavior, where asymptotic methods used to analytically solve fluid dynamic problems do not apply. We developed a mathematical model of this locomotion strategy using a system of nonlinear ordinary differential equations. We approximate the swimming legs as pairs of two-dimensional hinged oscillating plates following simple harmonic trajectories with background flow equal to the body velocity. The model accounts for forces on the paddles and on the body to predict the general planar motion in the sagittal plane. Propulsive forces on each paddling limb are calculated using drag-coefficient models, where the relationship between drag force and the Reynolds number is obtained from 2D computational fluid dynamics simulations. The model is currently limited based on the assumption that the total force produced is the sum of the forces produced by individual paddles, neglecting any fluid dynamic interactions that could augment force. A comparison of the swimming speed predicted by the model to that of a robotic model will be presented.