A long tradition of studies in both psychology and sociology has shown that social ties have positive effects on mental well-being of both the population in general and in educational contexts in particular. Specifically, researchers argue that mental well-being is systematically related to students' academic self-regulation. However, it is not clear how these three constructs are related, and what direct and indirect effects may exist from social ties to academic self-regulation. In the context of engineering education, this question is especially relevant because the literature has documented gaps in the formation of ties of minority social groups -such as women or ethnic groups- which could have effects on their mental well-being and their academic self-regulation. This work proposes a theoretical model in which the sense of belonging and sense of mattering have effects on mental well-being, while mental well-being has effects on students' academic self-regulation. This theoretical model was tested by using structural equation modeling, with data from an online survey applied to 1,872 engineering undergraduate students during the first semester of 2022. The main fit indicators of the model with the empirical data satisfactorily meet the cut-off criteria established (RMSEA=0.041; SRMR=0.038; CFI=0.998; TLI=0.998). The central effects proposed in the resulting theoretical model are statistically significant, both from the sense of belonging and mattering towards mental well-being, and from it towards academic self-regulation. This implies that there is an indirect effect from the sense of belonging towards academic self-regulation.