The simplest anharmonic characteristics of Ir and Rh are discussed in the framework of a previously developed simple pseudopotential model which describes the elastic moduli, phonon spectra and the lattice heat capacity in the harmonic approximation of these metals succesfully. The microscopic Gruneisen parameters, the dependences of the elastic moduli on pressure, the coefficient of thermal expansion and the equations of state at the finite temperatures have been calculated. The ab initio calculations of the energy-band structure and the equation of state for Ir at T=0 have been done to test the model for adequacy at high pressures. The values of different contributions (zero-point oscillations, quasiharmonic, etc.) in the considered thermodynamic characteristics of Ir and Rh are discussed.