Microsystems present several challenging reliability-related issues on account of their micron-scale dimensions. Many of these micron sized devices consist of compliant beam- or plate-like microstructures that are in close proximity to a substrate or other structural parts. If such structures come into contact, short-range adhesive forces can pin them together if they cannot be overcome by the elastic restoring forces of the deformed microstructures. This phenomenon of adhesion, often called stiction, depends on the structural response of the microstructure itself, as well as on the nature of the adhesive forces between the contacting surfaces. In this study we develop an approach to model adhesion in microsystems in a computationally feasible finite element environment, and demonstrate its capability via a companion experimental study. The modeling approach adopts the principles of three dimensional linear elastic fracture mechanics (LEFM) and extends it to thin-film plate-like microstructures. Extensive experimental work is done to study the behavior of adhesion in microstructure cantilever beams and square and circular plates. The finite element code is validated against analytically predicted and experimentally observed behavior to corroborate its effectiveness.