Various factors are inferred to influence the structural evolution of fold-and-thrust belts or thrust wedges, but the effects of lateral friction (such as that exerted by the opposite block of a strike-slip fault in nature or by sidewalls in analogue models) have rarely been given sufficient attention and hence are still far from being fully understood. Up to now, seaward-vergent and dually vergent thrust wedges have been satisfactorily explained by the classic Coulomb wedge theory and can be well reproduced in analogue and numerical models. In contrast, landward-vergent thrust wedges, which are uncommon in nature (e.g., those occurring in the Cascadia subduction zone), have not yet been adequately explained by the classic Coulomb wedge theory and can only be reproduced in a few analogue models under particular conditions. In order to look closer at the effects of lateral friction on the structural evolution of fold-and-thrust belts and to explore the origin of landward-vergent thrust wedges, we conducted a series of sandbox models under different conditions of lateral friction and various ratios of initial average lateral frictional stress to basal shear stress (τs/τd). Results of our models revealed that in the presence of a weak or ductile basal décollement, the direction of lateral friction can dictate not only the deformation propagation direction and the surface slope direction, but also the structural vergence of fold-and-thrust belts. Fold-and-thrust belts normally show a structural vergence in the same direction as the direction of lateral friction but a deformation propagation direction and surface slope direction opposite to the direction of lateral friction. According to the results of models and the relationships between structural vergence and lateral friction direction occurring both in Cascadia and the analogue models, we propose that an extremely high τs/τd ratio due to an extremely weak basal décollement and landward-directed lateral friction exerted by the opposite blocks of basement-involved strike-slip faults are probably the two key factors responsible for the origin of landward-vergent thrust wedges in Cascadia. This work illustrates that effects of lateral friction should be properly taken into account both in the kinematic analysis and designs of models to simulate fold-and-thrust belts in the presence of weak or ductile basal décollements.