The paper addresses the analysis and design of narrow cast in situ joints between precast concrete elements, in which continuity of reinforcement is achieved through overlapping headed bars. Using headed bars minimises the lap length required within the cast in situ joint region. The paper describes a non-linear finite-element model (NLFEM), which was used to simulate a series of tension splice tests carried out by the authors to simulate the tensile zone of a joint loaded in pure flexure. The tests studied the influences of concrete strength, transverse reinforcement, confining shear studs, headed bar spacing and lap length on joint strength. Results show that the NLFEM captures the behaviour of the joint well. Parametric studies are carried out with the validated numerical model to investigate the effects of variables not considered in the tests, such as shear stud size, cover and out-of-plane offset of the headed bars. The NLFEM provides otherwise unavailable insights into joint behaviour and is considered suitable for the design of standard joint configurations. Additionally, it can assist the development of design-oriented analysis methods.