Expressions for Mössbauer energy shift are obtained in a direct and simple form, at high, medium and low temperatures, using the infinite series expansion of the Debye integral, involving Bernoulli's numbers. The effect of pressure on the shift at low temperatures is arrived at through the dependence of the Debye temperature on pressure in the Grüneisen approximation. The effect of pressure on the energy shift is investigated for a number of radioisotopes in the pressure range of 0-300 kbar. Results for 57Fe are compared with earlier work. The variation of the Grüneisen parameter in terms of the atomic parameters of the elements is considered. It is felt that the value of the parameter for other elements also, obtained experimentally or otherwise can be analytically fitted and normalized to the obtained variation of the Grüneisen parameter.