Due to its extreme sensitivity and speed, the atomic force microscope (AFM) has recently emerged as an important tool in the measurement of surface stress. Fundamental to this application is theoretical knowledge of the effects of surface stress on the deflections of AFM cantilever plates. This is normally obtained by use of Stoney's equation, which is derived for a completely unrestrained plate. In this talk, the validity of Stoney's equation to rectangular and V-shaped AFM cantilever plates is investigated. It is found that use of Stoney's equation can lead to significant errors in measurements made using AFM cantilevers. Detailed finite element results and new analytical formulae, which replace Stoney's equation and greatly improve on its accuracy, shall be presented.