The main goal of this work is to present a methodology and a computer code which allow the designer, by means of optimization techniques, to obtain efficient shapes of plate and shell structures under linear-elastic behavior and dynamic loads. With this objective, it is used the optimization program SHELLD that includes the geometric modeling, the mesh generation, the structural analysis by the FEM, the sensitivity analysis and the structural optimization algorithm. In this thesis, the geometry of the free-form shell is represented by Coon surfaces, which are formed by two series of cubic splines intercepting the key points, which lay on the midsurface.Once the shell surface is discretized in finite elements, the structural analysis starts. The structural response analysis is performed by means of the Newmark direct integration method. The finite element used is the 9 nodes Huang-Hinton element, which belongs to the family of elements degenerated from 3D elements.The aim of the sensitivity analysis is to determine gradients of the objective functions and constraints of the design optimization problem with respect to the design variables. The method used in this work for performing the sensitivity analysis is based on the total differentiation of the discrete dynamic equilibrium equations and derivatives of stiffness, mass and damping matrices are performed by means of the finite difference method. This methodology is known in the literature as the Semi-analytical Method for sensitivity analysis. The sizing and shape variables are the thickness and the lengths of the radii in the key points respectively, which implies in a decrease of the number of variables in the project. The design of shell structures under dynamic loads is a common problem in engineering practice. In order to obtain an optimal design of these structures one generally tries to keep as low as possible their weight or volume, in one word their cost, while constraining their structural response in terms of displacements, accelerations, frequencies or stress resultants. Alternatively one can minimize the displacement or acceleration at some point of the structure or its global displacement while keeping its volume constant. In the case of free vibration the objective is to maximize the frequency, corresponding to the vibration mode one wants to stiffen, keeping the shell volume constant. In special cases of shells with multiple eigenvalues, try to keep as low as possible their volume considering frequency constrains to avoid clusters.To solve the nonlinear constrained optimization problem at hand the Sequential Quadratic Programming algorithm (SQP) from NAG library of FORTRAN is used. In this thesis, we have placed more emphasis on how to formulate optimization problems appropriately rather than on the theory underlying -mathematical programming- optimization algorithms, i.e. we use the SQP algorithm essentially as -black box-.