Specific Language Impairment (SLI), as many other cognitive deficits, is difficult to diagnose given its heterogeneous profile and its overlap with other impairments. Existing techniques are based on different criteria using behavioral variables on different tasks. In this paper we propose a methodology for the diagnosis of SLI that uses computational cognitive modeling in order to capture the internal mechanisms of the normal and impaired brain. We show that machine learning techniques that use the information of these models perform better than those that only use behavioral variables.