Selection in plant breeding is usually based on estimates of breeding values obtained with pedigree-based mixed models. These models have been used successfully for predicting breeding values in plants and animals. However, pedigree-based models cannot account for Mendelian segregation, a term that under an infinitesimal additive model and in the absence of inbreeding, explains one half of the genetic variability. Molecular markers (MM) allow tracing Mendelian segregation at several positions of the genome; potentially, this may increase the accuracy of estimates of genetic values and of the genetic progress attainable when these predictions are used for selection purposes. Genomic selection (GS) is an approach for improving quantitative traits that uses all available MM across the genome to estimate genetic values. In recent articles, validated GS in plant breeding using genomic regression and showed that models using MM were more accurate in predicting grain yield in wheat and maize than those based on pedigree only. With high-density markers, the number of markers exceeds the number of individuals, and estimation of marker effects via ordinary least squares is not feasible. Penalized regression, semi-parametric and their Bayesian counterpart are methods are available. Examples of the first group are Ridge regression, the Least Absolute Shrinkage and Selection Operator or the Elastic Net. In this presentation, we evaluate GS for grain yield in wheat and maize lines using different traits and various statistical models for studying the accuracy of the estimation of genetic values of genotypes that were not included in the data. Models are compared on the basis of predictive ability estimated using cross-validation methods. 1