Steel pipe jacking force calculation often ignores the lateral frictional resistance induced by the pipe horizontal deformation effect, resulting in insufficient prediction accuracy. To address this challenge, a soil pressure redistribution pattern for flexible pipe jacking is proposed based on the pipe-soil full-contact model, Spangler’s lateral deformation theory of buried flexible pipelines, pipe-soil coordinated interface contact, and soil arching effect. Next, an elastic center method is used to calculate the pipe horizontal deformation and soil pressure, and a surrounding soil pressure model is established for steel pipes considering the circumferential deformation effect. Subsequently, a novel calculation method for the lateral frictional resistance of pipe jacking is proposed considering the supporting and drag-reduction effects of slurry in the ring gap. Finally, a theoretical formula for the jacking force that considers the steel pipe horizontal deformation effect is established based on an existing face resistance model. The theoretical formula is verified by engineering cases, and parametric analysis is conducted simultaneously. The results show the following. (1) The calculation of steel pipe circumferential deformation should comprehensively consider the combined action of surrounding soil pressure and net buoyancy of pipes. The lateral soil pressure on the side of pipes can be calculated by multiplying the unilateral horizontal deformation by the soil reaction coefficient. In the engineering case, the steel pipe lateral deformation reaches 8‰ of the pipe diameter, and the maximum additional lateral soil pressure is up to 125.26 kN/m², which cannot be neglected. (2) The measured jacking force values are within the upper and lower limits calculated using the proposed formula. For the lower limit of the formula, the average calculation error is －19.3%, and the minimum error is －0.2%, which is superior to the code-specified formula and verifies the feasibility of the proposed model. The deformation effect on the jacking force is more pronounced under large burial depth, thin-walled steel pipe, and weak-stratum conditions. Meanwhile, the pipe-side soil pressure considering the pipe horizontal deformation effect is larger than the value calculated by the active earth pressure formula for rigid pipes, which is more consistent with the actual stress state of engineering practices.