In experimental designs, we encounter sometimes with problems in which the response variable is in linear relation with some other variables. These variables are called, covariates. Based on experimental conditions, these covariates are divided into the following two categories. 1) The covariates are stochastic such that they are not under the control of experimenter, however, one can observe them together with the response variables. 2) The covariates are not stochastic and are under the control of experimenter and their values are assigned by him. When the response variable is in linear relation with some variables, utilizing designs for models with covariates are useful. Using these designs, the mean square errors reduces and causes the appearance of real differences between the treatments. In this thesis, we take into account the covariates of type (2), and seek the optimal designs with covariates in block designs structure such that we find at the most efficient estimates for in the regression model parameters. In the first chapter, we introduce the basics of experimental designs with covariates and we give a short literature review of attentions made towards these designs. In chapter two, different block designs are considered and their structure are investigated, and the ways of constructing some of these designs are discussed. In the third, fourth and fifth chapters, some theorems about the block designs are presented. We also consider the construction of the matrix of covariates-values, under the certain conditions to have the most efficient estimation for the regression parameters in the block designs structure.