Reed valves in a compressor are critical parts that have a high fatigue failure potential due to cyclic bending and impact caused by the cyclic nature of the compression process. A sudden failure of a valve renders the compressor useless. Although the refining process of methods of fatigue design has already taken more than 50 years, older criteria such as Gerber and Goodman models are still attractive for engineering design of high cycle fatigue components. This paper presents an investigation on the effect of nonzero mean stress on the design of valve reeds that are widely used in compressors. The investigation relates the choice of a mean stress compensation models, with the predicted fluctuating bending fatigue strength and estimated safety coefficient values. The calculations have been performed using Gerber, Goodman, Soderberg, ASME, Crossland, and Tsapi-Soh models. The most relevant goal of this paper is to verify the efficiency of classical and advanced stress based multiaxial fatigue criteria to estimated value of fluctuating bending fatigue strength. The criterion proposed by Tsapi-Soh was found to gives estimated value of the fluctuating bending fatigue strength very close to the typical value from technical data and satisfying results in predicting the survival of the reed valves under bending fatigue failure.