Many engineering materials exhibit strong anisotropy along with a pressure dependence on the plastic yield behavior. The ability to predict the effects of pressure dependence and plastic anisotropy of these materials on their respective yield surfaces is important for accurately analyzing their behavior during deformation. The current work develops a general anisotropic yield criterion that includes the capability of modeling pressure-dependent effects either additively or multiplicatively in the yield criterion at the onset and during the evolution of plastic deformation. The developed yield criterion can be used to represent both quadratic and non-quadratic yield surfaces and has no restrictions on the symmetricity of the plastic behavior, allowing the entire spectrum from isotropic to fully anisotropic. The pressure dependence of the yield criterion and the corresponding plastic rate of deformation equation are expressed as general functional forms to allow development and incorporation of new pressure dependence functions or to accept existing pressure dependence functions directly. Therefore, the developed yield criterion can be used as a framework for accurately modeling the plastic behavior of various material systems, largely reducing the complexity in yield surface description for different classes of materials and allowing a systematic approach for implementation in numerical analysis procedures such as the finite element method. Two existing pressure-dependent models are reformulated to show the applicability of the general yield criterion framework presented herein to developing new non-quadratic anisotropic models with a dependence on pressure. While the general yield criterion is developed as an extension of a specific non-quadratic anisotropic yield criterion, the same model development methodology can be applied to other novel or existing yield criteria that are defined in the deviatoric stress space.