AbstractA simple theory is developed to study the pressure dependence of Grüneisen parameter, γ. The final results show that γ varies linearly with the pressure, that is, γ(p,T) = γ(0,T) – ηpwhere η is found to be a pressure‐independent but temperature‐dependent parameter. Moreover, it is shown that η is related to some other thermodynamic parameters and hence can have positive or negative magnitude which in turn will decide whether γ(p,T) decreases or increases with pressure. The calculated values of γ(p,T) in the whole range of pressure and temperature are found in very good agreement with the experimental results in case of all the solids studied like NaCl, CaF2, MgO, quartz, Na, K, and Li. Further, it is shown that the second Grüneisen parameter,q, and the Debye temperature, θ, can also be calculated as a function of pressure with the help of t