Population-based optimization methods like genetic algorithms and particle swarm optimization are very general and robust but can be costly since they require large number of function evaluations. The costly function evaluations can be replaced by cheaper models which are refered to as surrogate or meta models. Here we consider data-fitting models, particularly radial basis functions and kriging. We study the performance of these interpolation models on some analytical functions and aerodynamic data. Both the models have parameters which must be selected carefully to ensure good accuracy. For RBF, we implement a leave-one-out validation technique and for kriging, the parameters are determined by maximizing the probability density of the available data using a particle swarm optimization. The metamodels are then implemented in the shape optimization platform FAMOSA.