Using thermodynamic perturbation theory, we derive a simple formalism for treating intrinsic anharmonic effects in solids. In this formalism, the central quantity is the intrinsic anharmonicity parameter a, which can be derived from vibrational spectroscopy or computer simulation. Advantages of our approach include (1) correct low- and high-temperature behaviour, (2) analyticity of all the thermodynamic functions and (3) the possibility of systematic incorporation of higher-order anharmonic effects. This approach can be used in studying equations of state and thermodynamics of solids in a wide temperature range. A detailed comparison with other approaches is given.