In this chapter, we explore applications of type theory and abstract algebra to conceptual modelling in engineering. This chapter begins with a presentation of ideas for automatic model generation. The key concept is to analyse the formalisation mappings that appear in categories of mathematical models from a computer science perspective. These ideas naturally lead to the application of type theory to mathematical modelling. In this concept, mathematical models are formalised by types, and the type system of a functional programming language can be utilised to verify the consistency of model derivation. A general algorithm for such verification is presented in this chapter. Finally, a relational algebra-based approach to abstract description of models is proposed. While this approach lacks some strictness of the category theory-based modelling framework, it compensates with enhanced flexibility in working with models and relations between them. Moreover, even models of physical objects, which are not necessary described in terms of mathematical expressions and equations, can also be addressed by this approach.