The paper presents methods for the calculation of design velocity fields and mesh updating in the context of shape optimization. Velocity fields have a fundamental role in the integration of the main conceptual and software components in shape design optimization. Nonuniform rational B-splines are used to parameterize the domain boundary. A Newton/Raphson procedure is used to calculate the curve and surface internal parameters. A preconditioning iterative conjugate gradient method with low precision is used to improve the solution performance of the auxiliar problem in the calculation of the velocity fields. The velocity fields are also used to perturb the finite element mesh and element distortion measures are introduced. Finally, examples of two- and three-dimensional elastic problems are presented to illustrate the application of the algorithms.332147159