The efficiencies of single escape and double escape peaks were calculated by using Monte Carlo method and compared with measured efficiencies. The efficiency was obtained from the area ratio of escape peak to full energy absorption peak and the full energy absorption peak efficiency. For the escape peak interfered with other $gamma-ray$ peaks, the net area was obtained by area correction. The GEANT code developed in CERN was used for the Monte Carlo calculation. The calculated efficiencies of the escape peaks agreed with the measurement within $12\%$.