Accurate curvature estimation in mesh surfaces is an important problem with numerous applications. Curvature is a significant indicator of ridges and can be used in applications such as: recognition, adaptive smoothing, and compression. Common methods for curvature estimation are based on quadric surface fitting to local neighborhoods. While the use of quadric surface patches simplifies computations, due to its simplicity the quadric surface model is incapable of modeling accurately the local surface geometry and introduces a strong element of smoothing into the computations. Hence, reducing the accuracy of the curvature estimation. The method proposed in this paper models the local surface geometry by using a set of quadratic curves. Consequently, as the proposed model has a large number of degrees of freedom, it is capable of modeling the local surface geometry much more accurately compared to quadric surface fitting. The experimental setup for evaluating the proposed approach is composed of randomly generated Bezier surfaces for which the curvature is known with various levels of additive Gaussian noise. We compare the results obtained by the proposed approach to those obtained by other techniques. It is demonstrated that the proposed approach produces significantly improved estimation results which are less sensitive to noise.