Objective. To present a methodology based on the concept of Kronecker products that facilitates the construction of the variance and covariance matrix for designs with balanced data structure for 2 and 3 ways, and an application ​​in R to facilitate its calculation and application in different areas. Materials and methods. We provide a starting point for people interested in using R in the analysis of variance. Results. We use an application made ​​in R for a methodology based on Kronecker products through which we build the covariance matrix for working with designs with balanced data structure developed by Moya (2003). We also present an application of the method with real data. Conclusions. With this methodology we can accelerate the development and solution of some practical problems. The proposed methodology can be applied to mixed models with fixed or random effects with any number of factors.

Key words: Kronecker products, variance and covariance matrix, balanced designs, linear models, R Gui.