During oilfield drilling operations, the rock originally in the volume occupied by the wellbore is replaced by drilling fluid that exerts pressure on the borehole wall. This leads to a redistribution of stress in the vicinity of the wellbore, and may lead to yield of rock close to the borehole. This results in a decrease in stress near the borehole wall. This redistribution in stress is studied in this paper for a vertical well using a computational model that accounts for rock deformation and plastic strain in the near-wellbore region. The stress changes around the borehole lead to changes in elastic wave velocities that may be used to monitor the changes in stress that occur. The change in elastic wave velocities are sensitive to the mechanical properties of the rock, and may therefore be used to calibrate mechanical earth models used to predict rock failure due to production.