This paper presents a numerical method for structural optimization combining shape sensitivity analysis and the level-set method. The method is applied to linear and nonlinear elasticity problems in two and three dimensions. The objective functions considered include compliance, least square deviation from a target, and design-dependent loads. The shape derivative is computed using an adjoint method, and the free boundary is moved according to this derivative. The level-set method is used to track the boundary, and the evolution of the level-set function is governed by a Hamilton-Jacobi equation. The method is tested on various numerical examples, including a 2D cantilever, a 2D bridge, and a 3D cantilever. The results show that the method is effective for shape optimization and can handle topology changes. The optimal shape strongly depends on the initial guess, and the method is efficient in terms of computational cost. The paper also discusses the effect of different discretization schemes and reinitialization on the convergence of the optimization process.This paper presents a numerical method for structural optimization combining shape sensitivity analysis and the level-set method. The method is applied to linear and nonlinear elasticity problems in two and three dimensions. The objective functions considered include compliance, least square deviation from a target, and design-dependent loads. The shape derivative is computed using an adjoint method, and the free boundary is moved according to this derivative. The level-set method is used to track the boundary, and the evolution of the level-set function is governed by a Hamilton-Jacobi equation. The method is tested on various numerical examples, including a 2D cantilever, a 2D bridge, and a 3D cantilever. The results show that the method is effective for shape optimization and can handle topology changes. The optimal shape strongly depends on the initial guess, and the method is efficient in terms of computational cost. The paper also discusses the effect of different discretization schemes and reinitialization on the convergence of the optimization process.