Researchers have shown that the cracking related durability problems associated with cementitious materials can be mitigated through the use of self-healing systems. Many self-healing systems use embedded healing agents that are transported to cracks as they form. Inspired by biological materials, embedded vascular networks represent an effective way of transporting healing agents to the damage sites. The effectiveness of vascular self-healing systems is governed by the healing agent properties and the efficiency with which the network can supply the healing agent to the cracks. This study presents an unfitted finite element model for simulating healing agent transport in vascular self-healing materials [1]. The model employs a mixed-dimensional approach that couples the 3D flow in the cementitious matrix, governed by Richard’s equation, to the 2D crack-plane and 1D embedded vascular network flow, governed by the mass balance equation with Darcy’s law describing the healing agent flux. The flux between the matrix and crack-planes is described using an embedded discrete fracture approach, whilst a multi-point constraint unfitted finite element approach [2] is used to capture discontinuities, such as those associated with the healing agent interface, in the crack-plane and embedded vascular network flow. The performance of the model is demonstrated through the consideration of an experimental test concerning healing agent transport in a vascular self-healing cementitious specimen that was cracked under three-point bending. Following this, the model is used to investigate the effect of the vascular network architecture on the crack filling. The results show that the model can accurately reproduce experimentally observed behaviour and can prove a useful tool in the design and optimisation of vascular self-healing materials.