Soft biological tissues consist of cells and extracellular matrix (ECM), a network of diverse proteins, glycoproteins, and glycosaminoglycans that surround the cells. The cells actively sense the surrounding ECM and regulate its mechanical state. Cell-seeded collagen or fibrin gels, so-called tissue equivalents, are simple but powerful model systems to study this phenomenon. Nevertheless, few quantitative studies document the stresses that cells establish and maintain in such gels; moreover, most prior data were collected via uniaxial experiments whereas soft tissues are mainly subject to multiaxial loading in vivo. To begin to close this gap between existing experimental data and in vivo conditions, we describe here a computer-controlled bioreactor that enables accurate measurements of the evolution of mechanical tension and deformation of tissue equivalents under well-controlled biaxial loads. This device allows diverse studies, including how cells establish a homeostatic state of biaxial stress and if they maintain it in response to mechanical perturbations. It similarly allows, for example, studies of the impact of cell and matrix density, exogenous growth factors and cytokines, and different types of loading conditions (uniaxial, strip-biaxial, and biaxial) on these processes. As illustrative results, we show that NIH/3T3 fibroblasts establish a homeostatic mechanical state that depends on cell density and collagen concentration. Following perturbations from this homeostatic state, the cells were able to recover biaxial loading similar to homeostatic. Depending on the precise loads, however, they were not always able to fully maintain that state.