Abstract: During the construction of new tunnels undercrossing the existing tunnels, the predicted results of the stratum deformation are prone to large errors since the traditional stochastic medium theory cannot consider the influences of the existing tunnel. Considering the non-uniform convergence of the tunnel section after excavation, the traditional stochastic medium theory is simplified and improved based on the relationship between the key parameters of the stochastic medium theory and those of the Peck's formula. The heterogeneous strata and existing tunnels are equated by applying the bending stiffness of an existing tunnel and the equivalent layer method. A prediction model for the deformation of the existing tunnels and strata caused by the excavation of new undercrossing tunnels is proposed, and based on the relevant typical project, its accuracy is validated. The results show that compared with those of the traditional stochastic medium theory, the predicted curves of the proposed model are "wide and shallow" and have a greater correlation with the numerical calculations and the field measurements, and they have a higher rationality and accuracy, which may provide a theoretical basis for the prediction of the deformation of the existing tunnels and strata caused by the excavation of undercrossing tunnels.