A method for determining frequencies and vibration modes of the roof slab of shallowly buried underground structure is developed on the basis of the theory of transverse free vibration of Euler beam on elastic foundation.In view of the complexity of the determination of frequencies for roof slab of underground structure

this problem is assumed to be a plane strain problem.The free vibration equation of the roof slab of shallowly buried underground structure is derived.Then by using the boundary conditions

the frequency equation of the roof slab is obtained.Furthermore

the frequencies and vibration modes of the roof slab is obtained.It is concluded that the rotational stiffness of the side walls has negligible effect on the lower frequencies

but has great impact on the higher frequencies;moreover

the variation in frequencies of roof slab of underground structure with burying depth has been studied by considering the variation in soil stiffness with burying depth and the variation in attached mass of soil with depth burying due to the effect of soil arch.The obtained results may be used as a reference for the underground structure seismic design.