Kendall has used contact mechanics to show that surface energy affects the friction coefficient of a spherical particle on a smooth substrate. In particular, the friction coefficient is shown to depend on the particle diameter, the applied force and the interfacial energy. For small particles the friction coefficient can be twice that measured for large block samples. In the present analysis, contact mechanics is applied to determine the friction coefficient of an incompressible flat particle on a smooth compressible substrate. It is shown that the static friction coefficient of an incompressible truncated sphere (i.e. flat on the bottom) depends not only on the particle diameter, the applied force and the surface energy, but also on the elastic properties of the substrate. The author shows that a large enhancement in friction coefficient over that observed for bulk samples, in some cases a factor of two, can result for small flat particles on soft substrates. The implications for the effects of plasticisers and adsorbed solids and gases, and the choice of substrate material parameters, on friction are discussed.