A model for piezoelectric vibration energy harvesting with a piezoelectric cantilever beam is presented. The model incorporates expressions for variable geometry, tip mass, and material constants, and allows the parameterized determination of the voltage and power produced over a purely resistive load. The model is of a lumped-element form, with the base excitation acceleration and voltage representing the effort variables, and the tip velocity and electrical current representing the flow variables. Subsequent to the model's derivation, experimental results are presented and demonstrate the accuracy of the model. As peak power output for existing vibration configurations is typically of interest, several simple optimization studies are then performed on a simple generator configuration to demonstrate the effects of several of the driving geometric and material parameters.