Membrane shells embody architecturally expressive solutions, enabling a rich synthesis of structural efficiency and optimal use of material. Given the progressive demand for sustainable and innovative designs, the availability of computational tools capable of determining shell shapes with a selectively membrane bearing capacity is currently crucial in both architecture and engineering fields. In this respect, although methods condensating shells into simplified equivalent structures have been made available, the account of the actual physics of a funicular shell presupposes the treatment of an inherently ill-posed mathematical problem. To tackle this issue, the stress state is usually prescribed beforehand so that the static problem can be solved for the shell shape. Besides concealing the breach of trivial boundary conditions on complex domains, the user’s prescription of working stresses tends to subtly limit the solution space where the form-found geometry can be obtained. Further, under no instances, auxiliary functional requisites can be easily met. In this paper, a form-finding strategy of recent formulation is employed to study the effect of diverse velaroidal Airy stress functions on the form-finding of a funicular shell with predefined support extension. The proposed approach benefits from the embed of a nonlinear programming routine enabling the automatic computation of a feasible potential field under both static and user-defined functional constraints. Further, use is made of the isogeometric frame to attain accurate modelling and reduced computational effort.