By using a non-central force model proposed by the authors, the microscopic Gruneisen parameters gamma q,j and the effective value gamma G at different temperatures are calculated for silver, gold and aluminium in terms of elastic constants and their pressure derivatives. The microscopic Gruneisen parameters gamma q,j are calculated as a function of the wavevector q along the principal symmetry directions (100), (110), (111), (210), (211) and (221) and the values are averaged over a wavevector space in the first Brillouin zone by using the modified Houston's method for evaluation of integrals. The results obtained for gamma G show a fairly good agreement with the experimental values.