TheTrouton ratio, defined as the ratio of the extensional to the shear viscosity, may reach very high levels in viscoelastic media. Consequently the diagonal components of the deformation rate tensor, often of negligible importance in the analysis of flows ofNewtonian fluids, may be of primary interest here. Several significant phenomena unknown inNewtonian fluid mechanics are seen to have their origin in the tensile normal stresses generated by these extensional deformations of viscoelastic fluid media; they include the separation of particles or bubbles in accelerating flows (the „Uebler” effect), the operability of ductless siphons („Spinnbarkeit“) and, probably, turbulent drag reduction. A class of problems which may be treated by neglecting the usual shearing deformation rates and shearing stresses, and considering only the extensional behaviour of the medium, is identified. These problems are characterized by high values of the dimensionless elongation rate, defined as the product of the local extension rate and the natural time of the fluid. As this dimensionless group frequently reaches its highest levels in the primary fluid stream outside a boundary layer this approximation is termed an “Extensional Primary Field” or EPF approximation to focus attention on the primary or “outer” flow, as distinguished from flows in the vicinity of solid surfaces. The EPF approximation appears to provide a sufficient basis for analysis of several problems: converging flows into an orifice or duet from a larger reservoir, flows through porous solids and elongational flows with free surfaces as in textile fiber-spinning operations and flow in ductless siphons. In several other problems — lubricant squeeze films, turbulent flows under drag reducing conditions and flows about submerged objects — EPF considerations appear to be of importance but may not control the entire problem. The potential importance of EPF considerations in treating fluid mechanically controlled crystallization processes is noted.