The principle of coupled action of surrounding rock and support is a basic theory to accurate reveal that the tunnel is effectively supported by support structure. The longitudinal deformation profile (LDP) of tunnel roof radial displacement of a practical project has been calculated based on spatial effects of the excavation face and E. Hoek empirical equation. Mechanical model that describes the coupled action of surrounding rock and support has been built

and then the mathematical model that describe the relation of the tunnel roof radial displacement and virtual support force in mechanical model is built. The coupled action between surrounding rock and support in their whole interaction process is analyzed by analyzing and studying of mathematical and mechanical model. For the principle of coupled action of surrounding rock and support at elastioplastic deformation stage

the latest understanding has been given. The supporting action effect of a practical project has been calculated and analyzed by the research results. In this paper，the interaction solution of complete action process of surrounding rock and support at elastioplastic deformation stage has been obtained

and the interaction of surrounding rock and support also can be on-line predicted or reproduced by the research results.