A computational study of metal stepped surfaces has been performed with metal-metal interactions being described by Sutton and Chen potentials. The energetic parameters W0 and w(n) associated with the terrace-step-kink model have been determined for a variety of surfaces from energy minimization calculations. Comparison with available experimental data suggests that the elastic strain contribution to step-step repulsion is satisfactorily reproduced. In addition, the relaxational behaviour of the top most layers of such surfaces is also in accord with experiment. The molecular dynamics method has been used to study the step meandering process on the Pt(115), Pt(331), Pt(211) and Rh(211) surfaces. The degree of roughening and the characteristics of the rough surfaces above the step-roughening transition temperature are discussed. Also, it is found that the diffusion of surface matter is greater parallel to the steps than perpendicular to them and that this anisotropy of diffusion is surface and material dependent. On platinum, atoms can diffuse via exchange and chain-slippage mechanisms and these give rise to significant diffusion perpendicular to the steps, particularly on the Pt(115) surface. Such mechanisms are absent on rhodium due to the nature of the interactions between atoms and hence the observed anisotropy of diffusion was very high on Rh(211).