Mathematical models of interfacial roughness and interlayer diffusion and reaction, incorporated into the multilayer matrix method, in multilayer reflectors used in soft X-ray and EUV regions are created and discussed. Simulations on typical multilayers (e.g. Pt/a-Si, Pt/a-C and Ni/a-C) have revealed that the interfacial roughness reduces the peak reflectivity of a multilayer without a change of peak position, while the interlayer diffusion and reaction not only reduce the peak reflectivity sometimes (especially when diffusion occurs) but also shift the peak position. The interlayer diffusion causes more drastic change in multilayer performance than the interlayer reaction. The simulations on 'ideal' multilayer reflectors of commonly used materials (Pt, Mo, W, Ni, Cu) in conjunction with a-Si or a-C have also led to a recommended selection guide for material combinations over the wavelengths 3