An orifice rheometer was used to investigate the extensional properties of complex fluids at very high strain rates. It is based on the measurement of the pressure drop across a small size orifice as a function of the flow rate. Using flow simulations and the experimental pressure and flow rate data, an apparent extensional viscosity versus an apparent extensional rate was investigated for various fluids. This procedure was first tested for Newtonian fluids and excellent agreement was observed between the data and the simulation results. The flow through the orifice was found to be largely controlled by extensional components. The approach was then used to characterize the extensional properties of a polymeric solution (Boger fluid) and clay suspensions in a Newtonian fluid. The apparent extensional viscosity of these more complex fluids was found to be much larger than three times the shear viscosity, as predicted for Newtonian fluids by the Trouton relation.