We describe a dynamical model that predicts the zigzag motion of disks and oblate spheroids moving freely in a viscous liquid over a continuous range of aspect ratios and Reynolds numbers. This model combines the generalized Kirchhoff equations to describe the linear and angular momentum balances for the fluid-body system with a dynamical model for the wake-induced force and torque that incorporates the main characteristics of the wake dynamics deduced from previous experimental observations. The resulting model is shown to be able to reproduce quantitatively the oscillatory paths measured experimentally.