Based on a mangbody expansion of shortrange interatomic force,the fourbody interactions in compressed solid helium are computed by ab initio HartreeFock selfconsistent field technique and the atomic cluster method. It is concluded that fourbody terms give a repulsive contribution to the binding energy. By combination of the present manybody expansions with Aziz's longrange attractive potential, the equation of state(EOS) (T=0K) is calculated and compared with available experimental data. Results emphasize the importance of the fourbody interactions in compressed solid He. If only twobody interactions are included such as in the description of the helium gas, the pressure is much overestimated. Good agreement with experiments can only be extended up to about 10 GPa when the threebody corrections are added to; however, the predicted compression curve is obviously lower than that obtained in recent experiments at above 10 GPa. Our study shows that fourbody corrections can bring the calculated EOS into a good agreement with experimental data at pressures of 10\_27GPa. Our result also implies that the higherorder manybody effects should be taken into account at higher pressures.