The goal of this thesis is to develop a computationally inexpensive, accurate, and practical mathematical model of a hydraulic reed style check valve. While the modeling of disc style check valves is well represented in literature, reed valve modeling research has focused on applications in air compressors and internal combustion engines, where the working fluid has low density, viscosity, and bulk modulus. However, in a hydraulic system, the fluid – namely oil – is dense, viscous, and stiff, contributing additional physical effects that must be considered. Furthermore, the operating pressure in hydraulic systems is higher than in pneumatic systems, creating additional challenges from a structural perspective.In this thesis, a one degree of freedom hydraulic disc and reed style check valve model were developed using a hybrid analytical, computational, and experimental approach. The disc valve equation of motion was derived from Newton’s second law applied to the disc considering forces including pressure, spring reaction, and drag. Euler-Bernoulli beam theory was used to derive the reed valve equation of motion. In each case,the valve flow rate was modeled as quasi-steady orifice flow using an empirical discharge coefficient.