Temperature cycling has been shown to increase the incidence of intracellular ice at high subzero temperatures. The formation of intracellular ice is known to be lethal to cells except under special circumstances not encountered in cryosurgery. We introduce the concept of Dynamic Cryosurgery where the probe temperature is oscillated throughout the formation of the iceball which results in the propagation of thermal waves through the frozen tissue. Thermal waves may be propagated through frozen tissue to enhance the lethal formation of intracellular ice. We present a numerical algorithm that accurately predicts the 3-dimensional thermal distribution about a cryoprobe. Comparisons made between measured data and the simulated behavior of thermal waves in tissue show good agreement. Thermal waves rapidly attenuate with radial distance from cryoprobes and distort in shape. Their velocity is independent of amplitude but dependent on frequency. Constructive and destructive interference between thermal waves is shown to occur and implies that control of thermal waves to focus their lethal effects on designated regions of the frozen tissue is possible with multiple cryoprobes.