Substitution of the flow field U ( x,y,z,t )={ u ( x, y, t ), v ( x, y, t ), z γ ( x, y, t )} into the three-dimensional incompressible Euler equations generates a closed system of evolution equations, for the strain rate γ ( x, y, t ) and the two-dimensional vorticity ω ( x, y, t ), which are uniform in the z -direction. The system models a class of dynamical, stretched three-dimensional vortex flows that include Burgers9 vortices. Recent numerical simulations by Ohkitani & Gibbon have revealed that the strain rate γ ( x, y, t ) appears to develop a finite-time singularity, from smooth initial data, in the region where gamma is negative. Here, we prove that, for a large class of initial data, the support of γ - := max{0, - γ } necessarily collapses to zero in a finite time, while at the same time, the L 1 norm of γ - remains non-zero. Hence, γ - must necessarily become singular before or at the time of collapse. Our vortex flow represents one of a subclass of Euler solutions that have infinite energy. The fundamental question of finite-time singularity formation from smooth initial data for finite-energy three-dimensional Euler solutions remains the important open question.