Food pastes and suspensions are complex materials which are difficult to characterise in conventional rotational rheometry due to their complex microstructure and their usual tendency to slip at the wall. Squeeze flow, in which material flows between two circular plates as they are brought together, has traditionally been used as a way of overcoming these problems. Two squeeze flow rheometers were set up incorporating two novel pressuresensing devices, a strip sensor and a grid sensor. The strip sensor which measures the pressure distribution in the material along a radius, was found to be too sensitive to test fluids. The grid sensor which measures the whole two-dimensional pressure distribution in the material, was more robust and was validat~d using Newtonian silicone oils. Excellent agreement was found between the pressure sensor data and the well-known Stefan's theory, over the range of dimensionless times 0.4 to 0.8. On extension to non-Newtonian fluids, reasonable agreement was found between the well-known Scott's theory and the pressure data for a model pseudoplastic fluid, over an equivalent range of dimensionless times. The results for a paste material, however, did not agree well with Scott's theory. The flow regime in squeeze flow is different to that found in the simple shear flow of rotational rheometers. In squeeze flow the flow pattern changes from elongational to shear flow as the experiment progresses, which has two consequences: (i) it is unlikely that a single rheological equation could describe the flow over the whole experiment and (ii) the different flow regimes mean that comparison with rheological parameters obtained from conventional rheometry is unlikely to be successful.