Most of the Experiments contain studying the effects of two or more than two factors. Generally, for this kind of experiments, factorial designs are the most efficient. A factorial design is a design for which, in every complete experiment or replication of experiment, all of the possible combinations of the factor levels are studied. Usually, the observations are assumed to be independent. However, when we do experiments in real world, most of the times encompass with correlated observations. Thus, it is necessary to study designs which are more efficient when there exists a correlation. In this thesis, we study efficient factorial experiments whe data are spatially correlated. We also study the algorithms, such as exchange Algorithm, used to obtain optimal designs. The structure of spatially correlated data implies that the experiments should be done in the form of row-column design. Factorial experiments with spatially correlated data occur in many situations, particularly in agricultural field trials.