Conditional invertible neural networks (cINNs) were used for generative inverse design of aerodynamic shapes for a given aerodynamic performance target. The methodology was used to generate two-dimensional (2D) airfoil shapes for a target lift coefficient and three-dimensional (3D) vehicle shapes for a low drag vehicle given an aerodynamic drag coefficient target. Training data for both cases were generated for the forward process i.e., aerodynamic performance as a function of design variables that define the airfoil or vehicle shape, using design of experiments (DOE) and computational fluid dynamics (CFD) simulations. Due to the structure of the cINNs, the inverse process was learned implicitly, i.e., samples from latent space were transformed back to the design variables. The designs generated by the trained cINN model were simulated under identical conditions to check if they met the desired aerodynamic performance target. The distribution of design variables conditioned on a performance target learned by the cINN model was compared to the distribution in the training data. cINNs provide an easy-to-use tool to generate new designs that meet the desired aerodynamic performance, thereby, reducing the iteration time between aerodynamicists and stylists. In case of vehicle shape generation, since all generated vehicle shapes meet the aerodynamic performance target, the designer can select the shapes that do not conflict with other design constraints such as the interior volume, comfort, styling, and various safety requirements.