FERRE matches physical models to observed data, taking a set of observations and identifying the model parameters that best reproduce the data, in a chi-squared sense. It solves the common problem of having numerical parametric models that are costly to evaluate and need to be used to interpret large data sets. FERRE provides flexibility to search for all model parameters, or hold constant some of them while searching for others. The code is written to be truly N-dimensional and fast. Model predictions are to be given as an array whose values are a function of the model parameters, i.e., numerically. FERRE holds this array in memory, or in a direct-access binary file, and interpolates in it. The code returns, in addition to the optimal set of parameters, their error covariance, and the corresponding model prediction. The code is written in FORTRAN90.