A regular patch is a patch for which the Jacobian has rank 2 for all . A patch is said to be regular at a point provided that its Jacobian has rank 2 at . For example, the points at in the standard parameterization of the sphere are not regular.

An example of a patch which is regular but not injective is the cylinder defined parametrically by with and . However, if is an injective regular patch, then maps diffeomorphically onto .