We describe studies of the effects of point defects on a t-J model of high Tc superconductors. One kind of point defect is associated with an enhanced value of J at certain randomly selected sites. The other kind of defect is associated with random values of the on site energy in the one-electron part of the model, as in the Anderson model of localization. We present a qualitative argument to the effect that such a model might account for the anomalous sensitivity of high Tc superconductors to nonmagnetic impurities in the copper oxide planes. We present numerical mean field calculations on the model in which disorder due to point defects is treated explicitly. A strong dependence of Tc on the Anderson parameter W is observed.