In the framework of effective-mass envelope function theory, the valence energy subbands and optical transitions in lateral superlattices (LSLs) have been calculated by the plane-wave expansion method. The effects of finite offset and valence band mixing are taken into account. The modulations of several types of lateral potential are also evaluated; they indicate that the out-of-phase modulation on either side of the wells is the strongest while the in-phase modulation is the weakest. The lateral modulation periods have a weak effect on the lowest hole energy levels. When one is making LSLs, the fabrication can be tailored to make the lateral modulation period fairly large, which is favourable for technological applications. Our calculations also show that the effect of the difference between the effective masses of holes in different materials on the valence subband structures is significant. Our theoretical results are in agreement with the available experimental data and have great significance as regards investigating and making low-dimensional semiconductor devices.