One of the most important design issues for filament-wound hydrogen storage vessels reflects on the determination of the optimal winding trajectories. The goal of this paper is to determine the optimal fiber paths and the resulting laminated structures for non-geodesically overwound circular toroidal hydrogen storage vessels. With the aid of the continuum theory and the non-geodesic law, the differential equations describing non-geodesic paths on a toroidal surface are given. The general criteria for avoiding fiber-bridging and slippage on a torus are formulated by differential geometry. The relation between the slippage coefficient and the winding angle is obtained to meet stable winding requirements. The initial winding angle and the slippage coefficient of non-geodesics are considered as the design variables, while the minimum shell mass acts as the objective function. The optimal non-geodesic trajectories, corresponding to various relative bending radii, are determined in order to evaluate the effect of non-geodesics on the structural performance of toroids. Results indicate that circular toroidal vessels designed using the present method show better performance than geodesics-based ones, mainly triggered by maximum utilization of the laminate strength. The results also reveal that the structural efficiency of circular toroidal vessels can be significantly improved using non-geodesic winding. (C) 2009 Professor T. Nejat Veziroglu. Published by Elsevier Ltd. All rights reserved.