This article aims to show the effectiveness of evolutionary algorithms in automatically parsing sentences of real texts. Parsing methods based on complete search techniques are limited by the exponential increase of the size of the search space with the size of the grammar and the length of the sentences to be parsed. Approximated methods, such as evolutionary algorithms, can provide approximate results, adequate to deal with the indeterminism that ambiguity introduces in natural language processing. This work investigates different alternatives to implement an evolutionary bottom-up parser. Different genetic operators have been considered and evaluated. We focus on statistical parsing models to establish preferences among different parses. It is not our aim to propose a new statistical model for parsing but a new algorithm to perform the parsing once the model has been defined. The training data are extracted from syntactically annotated corpora (treebanks) which provide sets of lexical and syntactic tags as well as the grammar in which the parsing is based. We have tested the system with two corpora: Susanne and Penn Treebank, obtaining very encouraging results.