Design of perforating for optimal productivity is currently based on semi-analytical techniques or charts developed with the use of finite element models. Both methods are severely restricted by their limiting assumptions, while the direct use of finite element models is impractical for field design work. This paper describes the development and application of two new, practical finite difference models for the determination of the productivity of single perforation and multi-perforation systems in single phase as well as multiphase flow. The first models flow through laboratory cores. The second models multiple perforations in a field context. The latter allows any arbitrary perforation geometry, including irregular spacing; gun eccentricity; gravel packed completions; drilling damage; and complex reservoir heterogeneity. In addition, the field model can be applied to vertical or horizontal wells, and can be also used for analyzing RFT pressure tests. The models have been tested and validated against published results including laboratory cores and perforated completions. The validation and application work has yielded a number of interesting findings and some important practical implications for perforating design.