Simulations based on time-dependent Ginzburg–Landau theory are employed to determine the critical current for a model system which represents a Nb–Ti-like pinning landscape at low drawing strain. The system consists of ellipsoids of normal metal, with dimensions 60ξ × 3ξ × 3ξ, randomly distributed throughout the superconducting bulk with their long axes parallel to the applied current and perpendicular to the field. These preciptates represent the α-Ti elongated precipitates which act as strong pinning centres in Nb–Ti alloys. We present the volume pinning force density as a function of field across the entire range of precipitate volume fractions and find that optimised material in our model system occurs at 32 vol.% ppt., whereas in real materials the optimum occurs at 25 vol.% ppt. The maximum pinning force density in our simulations is slightly higher (5.4 × 10−3 JDBc2 vs. 17 GN·m−3 = 4.5 × 10−3 JDBc2) and occurs at a lower reduced field (0.2Bc2 vs. 0.5Bc2) than in real materials. We conclude that the broad features of Nb–Ti-like systems are captured in our model, but that the details of the precipitate pinning mechanism are not yet included properly.