Word order is one of the most readily observed aspects of the syntax of human language. This thesis focuses on intralinguistic word order variation and, in particular, on a tendency - known as dependency length minimisation (DLM) - for words and phrases that are close in the syntactic structure to be linearly adjacent. Our approach to DLM phenomena in word order variation is computational: the use of syntactically-annotated corpora and statistical methods allows for generalisations of the variation principles across dozens of languages. This thesis presents three cross-linguistic computational studies at three levels of linguistic representation. First, we look at word order variation at the language level and compare the extent to which languages follow the DLM principle. Secondly, we investigate DLM effects in adjective variation across five Romance languages. Finally, we present a model of incremental production of word order which incorporating word order variation and dependency length effects.