Abstract: The current studies on the cavity expansion in sand have not considered the breakage and dilatancy of sand particles. In order to facilitate the subsequent calculation, many scholars have simplified the calculation parameters such as shear stress and shear modulus, so the final results do not reflect the actual situation accurately. In response to the above problems, a critical constitutive model for sand considering particle breakage and dilatancy is used. Employing the associate flow rules and the Lagrangian analysis method in the plastic zone, the cylindrical cavity expansion problem described by the traditional Euler description is converted into a first-order nonlinear ordinary differential equation with the initial values based on the Lagrangian description. Finally, the semi-analytical exact solution to the cylindrical cavity expansion problem in sand is obtained by the numerical method, and the influences of the initial stress on the cavity expansion results are analyzed through an example. The results show that the particle breakage and the initial stress have great influences on the cavity stress and the radius of the plastic zone. The combination of particle breakage and initial stress causes the soil to exhibit different dilatancy characteristics during cavity expansion. In addition, the sand under high initial stresses is difficult to reach the critical state during cavity expansion.