Embodied approaches to language understanding hold that comprehension of linguistic material entails a situated simulation of the situation described. Some recent studies have shown that implicit, explicit, and relational properties of objects implied in a sentence are part of this simulation. However, the issue concerning the extent to which language sensorimotor specificity expressed by linguistic constituents of a sentence, contributes to situating the simulation process has not yet been adequately addressed. To fill this gap, we combined a concrete action verb with a noun denoting a graspable or non-graspable object, to form a sensible or non-sensible sentence. Verbs could express a specific action with low degrees of freedom (DoF) or an action with high DoF. Participants were asked to respond indicating whether the sentences were sensible or not. We found that simulation was active in understanding both sensible and non-sensible sentences. Moreover, the simulation was more situated with sentences containing a verb referring to an action with low DoF. Language sensorimotor specificity expressed by the noun, played a role in situating the simulation, only when the noun was preceded by a verb denoting an action with high DoF in sensible sentences. The simulation process in understanding non-sensible sentences evoked both the representations related to the verb and to the noun, these remaining separated rather than being integrated as in sensible sentences. Overall our findings are in keeping with embodied approaches to language understanding and suggest that the language sensorimotor specificity of sentence constituents affects the extent to which the simulation is situated.