  The effect of pressure on the thermal expansion of solid CH$_4$ is calculated
for the low temperature region where the contributions from phonons and librons
can be neglected and only the rotational tunnelling modes are essential. The
effect of pressure is shown to increase the magnitude of the peaks of the
negative thermal expansion and shifts the positions of the peaks to the
low-temperature region, which goes asymptotically to zero temperature with
increasing pressure. The Gruneisen thermodynamical parameter for the rotational
tunnelling modes is calculated. It is large, negative, and increases in
magnitude with rising pressure.
