Using a large set of ray tracing in N-body simulations, we examine lensing profiles around massive dark haloes in detail, with a particular emphasis on the profile at around the virial radii. We compare radial convergence profiles, which are measured accurately in the ray-tracing simulations by stacking many dark haloes, with our simple analytic model predictions. Our analytic models consist of a main halo, which is modelled by the Navarro–Frenk–White (NFW) density profile with three different forms of the truncation, plus the correlated matter (two-halo term) around the main halo. We find that the smoothly truncated NFW profile best reproduces the simulated lensing profiles, out to more than 10 times the virial radius. We then use this analytic model to investigate potential biases in cluster weak lensing studies in which a single, untruncated NFW component is usually assumed in interpreting observed signals. We find that cluster masses, inferred by fitting reduced tangential shear profiles with the NFW profile, tend to be underestimated by ∼5–10 per cent if fitting is performed out to ∼10–30 arcmin. In contrast, the concentration parameter is overestimated typically by ∼20 per cent for the same fitting range. We also investigate biases in computing the signal-to-noise ratio of weak lensing mass peaks, finding them to be ≲4 per cent for significant mass peaks. In the appendices, we provide useful formulae for the smoothly truncated NFW profile.