We use a three-dimensional finite element model for viscous flow to investigate the lateral linkage mode of two initially isolated fold segments. Depending on the separation distance between the fold hinge lines, four different fold linkage scenarios are observed. Linear linkage yields a sub-cylindrical fold with a saddle at the location where the two initial folds linked. Oblique linkage produces a fold resembling a type II refold structure. Oblique–no linkage results in two curved folds with fold axes plunging in opposite directions. Linear–no linkage yields a fold train of two separate subcylindrical folds with fold axes plunging in opposite directions. Representative numerical models for detachment and matrix folding for both power-law and linear viscous rheologies exhibit the same four fold linkage modes. The transition from linkage to no linkage occurs when the fold separation between the initially isolated folds is slightly larger than one-half of the low-amplitude fold wavelength. We demonstrate a natural example of lateral fold linkage from the Kurdistan region of Iraq, and point out the economic interest of saddle points linking the initially isolated fold segments.