We analyse the singularity formation of congruences of solutions of systems
of second order PDEs via the construction of \emph{shape maps}. The trace of
such maps represents a congruence volume whose collapse we study through an
appropriate evolution equation, akin to Raychaudhuri's equation. We develop the
necessary geometric framework on a suitable jet space in which the shape maps
appear naturally associated with certain linear connections. Explicit
computations are given, along with a nontrivial example