We have made anharmonic calculations of phonon frequency shifts and widths, the thermal strain, and the lattice heat capacity for solid rubidium. The calculations were performed using an interatomic potential derived from the work of Price, Singwi, and Tosi. The calculated shifts are in reasonable agreement with experiment, except in the case of the Σ4 transverse branch in the [ζζ0] direction, where there are definite indications that the calculation disagrees with experiment. The calculated thermal strain is ~15% too high at intermediate temperatures. On the other hand, the calculated anharmonic contributions to the heat capacity are in good agreement with experiment at intermediate temperatures, but are 10 to 20% too low near the melting temperature. The anharmonic contributions are sensitive to the third and fourth derivatives of the potential, owing to the large degree of cancellation between the cubic and quartic terms. Furthermore there is evidence that higher order anharmonic terms may be significant.