Microcontact printing (MicroCP) is a form of soft lithography that uses the relief patterns on a master polydimethylsiloxane (PDMS) stamp to form patterns of self-assembled monolayers (SAMs) of ink on the surface of a substrate through conformal contact. Pyramidal PDMS stamps have received a lot of attention in the research community in recent years, due to the fact that the use of the pyramidal architecture has multiple advantages over traditional rectangular and cylindrical PDMS stamps. To better understand the dynamic MicroCP process involving pyramidal PDMS stamps, in this paper, numerical studies on frictionless adhesive contact between pyramidal PDMS stamps and transversely isotropic materials are presented. We use a numerical simulation method in which the adhesive interactions are represented by an interaction potential and the surface deformations are coupled by using half-space Green's functions discretized on the surface. It shows that for pyramidal PDMS stamps, the contact area increases significantly with increasing applied load, and thus, this technique is expected to provide a simple, efficient, and low-cost method to create variable two-dimensional arrays of dot chemical patterns for nanotechnology and biotechnology applications. The DMT-type and Johnson–Kendall–Roberts (JKR)-type-to-DMT-type transition regimes have been explored by conducting the simulations using smaller values of Tabor parameters.