The following study presents single and multipoint aerodynamic shape optimizations of two benchmark problems defined by the Aerodynamic Design Discussion Group (ADODG). Mesh warping and geometry parametrization is accomplished by fitting the multi-block structured grid to a B-spline volumes and performing the mesh movements by using surface control points embedded with free-form deformation (FFD) volumes. The aerodynamic model solves the RANS equations with Spallart-Almaras turbulence model. A gradient based optimization algorithm is used with an adjoint method in order to compute the objectives and constraints derivatives with respect to the design variables. The objective in this work is to minimize the drag of airfoil and wings for transonic regimes taking into account volume and thickness constraint, including aerodynamic coefficients constraint. The first problem solved is RAE2822 airfoil in viscous transonic flow, with a lift constraint. The shock in the upper surface is eliminated and the drag coefficient is reduced by 50%. Also in this problem we started the optimization solution from a circle in order to check the robustness of both the flow solver and the mesh warping algorithm, while reaching a "close" solution as obtained by starting from rae2822 airfoil. The second problem is single and multi-point lift and pitch moment constrained drag minimization of the Common Research Model (CRM) wing in transonic, viscous flow. The CRM design is very challenging due to the tight coupling between aerodynamic performance, trim and stability. Other design challenges include the number of design variables and its effect on the optimized configuration. The single-point optimization reduced the drag coefficient by 7.7% using 192 design variables. The single-point designs are relatively robust to the flight conditions. Further robustness is achieved through a multi-point optimization with nearly 5% drag reduction.