The presence of a capsule around a tumor is known to be correlated with benign status, and the absence of a capsule often has negative implications for patient prognosis. A mechanical description is presented of the growth of a tumor and the resulting deformations of surrounding normal tissue. A mathematical model of the mechanics is analyzed using physical parameters measured in vivo and in vitro. The model has only three dimensionless parameters, and its results are very robust with respect to parameter variation. We show that the presence of contractility in the surrounding tissue, corresponding to a host defense, can make an existing capsule denser and constrain the tumor better, but cannot be responsible for the observed pressure gradients in encapsulated tumors. Some implications for treatment are discussed.