The unchecked growth of a solid tumor produces solid stress, causing deformation of the surrounding tissue. This stress can result in clinical complications, especially in confined environments such as the brain, and may also be responsible for pathophysiological anomalies such as the collapse of blood and lymphatic vessels. High stress levels may also inhibit further cell division within tumors. Unfortunately, little is known about the dynamics of stress accumulation in tumors or its effects on cell biology. We present a mathematical model for tumor growth in a confined, elastic environment such as living tissue. The model, developed from theories of thermal expansion using the current configuration of the material element, allows the stresses within the growing tumor and the surrounding medium to be calculated. The experimental observation that confining environments limit the growth of tumor spheroids to less than the limit imposed by nutrient diffusion is incorporated into the model using a stress dependent rate for tumor growth. The model is validated against experiments for MU89 tumor spheroid growth in Type VII agarose gel. Using the mathematical model and the experimental evidence we show that the tumor cell size is reduced by solid stress inside the tumor spheroid. This leads to the interesting possibility that cell size could be a direct indicator of solid stress level inside the tumors in clinical setting.