In this paper, the conduct of the split-plot designs with t he main treatments disposed in balanced incomplete blocks,was analised. For this, the following mathematical model, was used: y_ijs = m + t_i + b_j + e _k(ij) + t’_s + (tt’) _is + e _ijs wherw, for i=1, 2,..., v; j=1, 2, ..., u ; k=1, 2,..., k, y_ijs denotes the observation of the subplot containing the s th subtreatment of the i th main treatment in the j th block; m denotes the effect of general mean; t_i denotes the effect of the i th main treatment; b_j denotes the effect of the j th block; e _ij denotes the error inherent at the k th whole-plot of the j th block in the i th mean treatment, characterized with a error (a) component; t'_s denotes the effect of the s th sub treatment; (tt') _is denotes the effect for the interaction between i th main treatment and s th sub treatment; e_ijs denotes the error inherent at the i-j-s th sub plot, characterized with a error (b) component. Moreover, the presence of constant correlaction, p, between two subplots of sarne plot, and independence among subplots of the distincts plots, was considered, resulting: (See Thesis). ln methodology one split-plot design with the v main treatments disposed in r out of a balanced incomplete block (r< a), where every block was formed by k plots, and every pair of main treatments occurred in λ blocks, was considered. Under these assumptions, the solution of the normal equations, the dispersion matrix for the effects in the mathematical model proposed, the criterion for the usual null hypothesis tests and the criterion of the multiple comparisions by Tukey's test based on linear functions variance, was obtained. Except for constants inherents in the model, two main conclusions were obtained: estimates of main treatments and blocks, obtained in this study, were analogous to those existent in the literature of the balanced incomplete block design; while other estimates were analogous to those correspondents in the split-plot randomized block design.