High-throughput screening techniques for cellular response are often unable to account for several factors present in the in vivo environment, many of which have been shown to modulate cellular response to the screened parameter. Culture in three-dimensional biomaterials and active mechanical stimulation are two such factors. In this work, we integrate these microenvironmental parameters into a versatile microfabricated device, capable of simultaneously applying a range of cyclic, compressive mechanical forces to cells encapsulated in an array of micropatterned biomaterials. The fabrication techniques developed here are broadly applicable to the integration of three-dimensional culture systems in complex multilayered polymeric microdevices. Compressive strains ranging from 6% to 26% were achieved simultaneously across the biomaterial array. As a first demonstration of this technology, nuclear and cellular deformation in response to applied compression was assessed in C3H10T1/2 mouse mesenchymal stem cells encapsulated within poly(ethylene glycol) hydrogels. Biomaterial, cellular, and nuclear deformations were non-linearly related. Parametric finite element simulations suggested that this phenomenon was due to the relative stiffness differences between the hydrogel matrix and that of the encapsulated cell and nucleus, and to strain stiffening of the matrix with increasing compression. This complex mechanical interaction between cells and biomaterials further emphasizes the need for high-throughput approaches to conduct mechanically active experiments in three-dimensional culture.