  The equations of a planar elastica under pressure can be rewritten in a
useful form by parametrising the variables in terms of the local orientation
angle, $\theta$, instead of the arc length. This ``$\theta$-formulation'' lends
itself to a particularly easy boundary layer analysis in the limit of weak
bending stiffness. Within this parameterization, boundary layers are located at
inflexion points, where $\theta$ is extremum, and they connect regions of low
and large curvature. A simple composite solution is derived without resorting
to elliptic functions and integrals. This approximation can be used as an
elementary building block to describe complex shapes. Applying this theory to
the study of an elastic ring under uniform pressure and subject to a set of
point forces, we discover a snapping instability. This instability is confirmed
by numerical simulations. Finally, we carry out experiments and find good
agreement of the theory with the experimental shape of the deformed elastica.
