Stamp deformation can affect the dimensional stability of the microcontact printing process. We consider limitations imposed due to reversible deformation of a single stamp. Detailed analyses of several modes of stamp deformation have been carried out. Stability criteria have been obtained for both vertical and lateral collapse of surface relief features, including buckling. The shape change of surface features imposed by surface tension has been analyzed, and the corresponding internal stresses are given in closed form. The residual stresses induced by chemical and thermal shrinkage when the elastomeric stamp is bonded to a stiff substrate are analyzed. In addition, the relation between applied load and displacement of a stamp supported by a stiff substrate is given in closed form. Contact stresses between the stamp and substrate have been analyzed both analytically and numerically by a finite element method. The role of adhesion in determining the contact area is clarified. The effect of surface roughness on the contact mechanics has been studied, and closed form solutions have been obtained for surface asperities that are periodically distributed. The contact mechanics of stamps with smooth relief features has been studied, and the dependence of contact area on the work of adhesion and the applied pressure is given in closed form. The force required to separate the stamp from the substrate has been estimated using a fracture mechanics approach. The stability and contact mechanics results are summarized by a stability and contact map.