Abstract In this study, the methods for constructing accurate and consistent geometrical and finite element (FE) models for general cracked tubular Y-joints are described. Firstly, geometrical analysis of welded tubular joint is given and it is then extended to the modelling of general cracked Y-joints. The concept of crack surface and a simple mapping approach are suggested to model either through-thickness or surface cracks which can be of any length and located at any position along the brace–chord intersection. Secondly, the geometrical model developed will be used in the generation of consistent FE meshes. The basic concepts used for the design and generation of three-dimensional FE meshes will be described. This will include the meshing procedures for discretization of tubular joints with through-thickness and surface cracks which are frequently regarded as one of the most difficult steps in the construction of tubular joint models. Finally, some mesh generation examples for uncracked and cracked Y-joints will be presented to demonstrate the use of the purposed geometrical model and mesh generation scheme developed.