Abstract <p>This work is devoted to a hypersonic flow around curved two-dimensional pointed bodies. The generated intense leading shock wave is considered to be attached to the tip of the body. In gas dynamics, the thin shock layer method is mostly used to construct approximate analytical solutions for problems with strong shock waves. In this case, the small parameter is the ratio of gas densities before and after the emerging strong discontinuity. By using the thin shock layer method to solve a nonlinear system of gas dynamics equations it is possible to construct a mathematical model of the flow. Analysis of the boundary conditions makes it possible to determine the type of series expansion of the required quantities in powers of the small parameter and to construct approximate analytical solutions. This work presents an approximate solution of the problem of a flow around a pointed body moving at a high variable velocity. It is assumed that the shape of the body differs little from a body with a straight generatrix. The solution of the problem is constructed in Lagrangian variables. The planar and axisymmetric cases are considered.</p>