This paper reports a new method of thin film encapsulation for surface micromachined sensors using an epitaxially grown polysilicon cap layer. This technique saves die area and enables the sensors to be handled in standard mounting processes such as pick and place and is suitable for injection plastic molding. The 'epipoly' encapsulation is designed for a lateral piezoresistive accelerometer, but is broadly applicable. This paper presents an analytic model that describes the deflection of the epipoly encapsulation as a function of pressure, thickness, length, shape, standoff height, venting, sealing, and material properties. This model is verified with Finite Element Analysis (FEA) and experiment.