In order to research into initial latent causes of roof damage for some Grotto No.4

the viscoelastic thin plate theory is used for setting up analytical solution of viscoelastic deformation and stress for the generalized Kelvin model

based on the laws of deformation and damage and structural boundary conditions for Grotto No.4 .To obtain the stress field and the displacement field of whole region at any time

a searching method of analytical total area point by point is presented

in which total region is divided into many small zones and each zone stress and each gridpoint displacement are calculated by given analytic formulas. By calculation and analysis，the displacement field and varied deformation and tensile damage region with time are given for the grotto top plate

where two dividing lines of possible tensile damage region are almost identical with in-situ measurement. This shows the boundaries of initial tensile region are unstable source of later real damage. The conclusion is useful to protecting and maintaining the grottoes. The case analysis has shown that presented model and analytical method are correct and rational. The method and conclusion can be in common use.