Statistical methods are developed to model random processes on multidimensional Euclidean space from observed data. Statistical inference techniques are used to estimate model parameters and test hypotheses concerning stationarity, isotropy, and number of parameters. Algorithms are described for fitting parametric models and testing between alternative model structures. Stochastic partial difference equation models of multidimensional processes are discussed in detail. Computer generated data from a known model are used to directly demonstrate the statistical procedures.