Three topics are considered in this thesis. The first is evaluation of the effective elastic moduli of porous materials and considers materials such as porous glass, sandstone, sintered bronze and iron materials, porous ceramics. Models with spherical pores were first considered showing good agreement for some materials but not for materials prepared by powder sintering. A number of modifications of increasing complexity were introduced accounting for non-spherical pores and their interaction. The models then compare well with experimental data for sintered materials. The other topics of the thesis can be used to model mixed lubrication in plain bearings where part of the load is carried by contacting asperities and part by the lubricant film. The roughness features affect the ability of the lubricant to flow in the gap between the surfaces and surface deflection is caused by asperity contact pressures only. A method is presented to solve dry contact problems for nominally plane surfaces using a simple elastic-plastic model at asperity contacts and a differential formulation for the elastic deflection. Periodic roughness defined over a representative area is incorporated using Fourier transforms to calculate the convolutions. The method is validated by comparison with the results of an elastic-plastic rough surface contact analysis obtained using a finite element method. A method is then developed to model the mixed lubrication problem based on the homogenised Reynolds equation where the effect of the roughness features is isolated from that of the global geometry of the bearing. Local rough problems are solved and the average effect of the roughness on lubricant flow expressed in terms of flow factors, which are functions of global film thickness. When direct asperity contact occurs the deflected shape is obtained from dry contact analysis of the representative roughness area. The global problem is then solved using the Reynolds equation modified with appropriate flow factors taking the mean contact pressure obtained from the local problem into account in load determination. The homogenised method is validated against the series of deterministic solutions and cases of surfaces with measured roughness are presented.