This paper reports the flow behaviour of Newtonian and Boger fluids through various axisymmetric contraction configurations by means of numerical predictions. A principal aim has been to evaluate the geometrical design choice of the hyperbolic contraction flow. The FENE-CR model has been used to reflect the behaviour of Boger fluids, with constant shear viscosity, finite (yet large) extensional viscosity and less than quadratic first normal stress difference. Numerical calculations have been performed on six different contraction configurations to evaluate an optimized geometry for measuring extensional viscosity in uniaxial extensional flow. The influence of a sharp or rounded recess-corner on the nozzle has also been investigated. Few commercial measuring systems are currently available for measurement of the extensional rheology of medium-viscosity fluids, such as foods and other biological systems. In this context, a technique based on the hyperbolic contraction flow would be a suitable alternative. The pressure drop, the velocity field, the first normal stress difference and the strain rate across the geometry have each been evaluated for Newtonian and Boger fluids. This numerical study has shown that the hyperbolic configuration is superior to the other geometry choices in achieving a constant extension rate. In this hyperbolic configuration, no vortices are formed, the measuring range is broader and the strain rate is constant throughout the geometric domain, unlike in the alternative configurations tested. The difference between sharp and rounded recess-corner configurations proved to be negligible and a rise in excess pressure drop (epd) for increasing deformation rates has been observed.