  We develop and analyze a discontinuous Petrov--Galerkin method with optimal
test functions (DPG method) for a shallow shell model of Koiter type. It is
based on a uniformly stable ultraweak formulation and thus converges robustly
quasi-uniformly. Numerical experiments for various cases, including the
Scordelis--Lo cylindrical roof, elliptic and hyperbolic geometries, illustrate
its performance. The built-in DPG error estimator gives rise to adaptive mesh
refinements that are capable to resolve boundary and interior layers. The
membrane locking is dealt with by raising the polynomial degree only of the
tangential displacement trace variable.
