Comprehending a mathematical modelling task is a central prerequisite for the following modelling process. In this study, we investigated the roles that the language proficiency of the students and the linguistic wording of the task play for the comprehension and the successful solving of mathematical modelling tasks. Five mathematical tasks with a constant modelling complexity and a varied linguistic complexity were developed. 634 students of comprehensive schools were tested and their socio-demographic factors as well as their language proficiency were measured. The results show a strong relationship between language proficiency and mathematical modelling achievement. Moreover, the findings suggest that increasing the linguistic complexity of mathematical modelling tasks results in lower solution frequencies.