The present investigation deals with the study of plane waves and fundamental solution in a modified couple stress generalized thermoelastic solid with mass diffusion. It is found that for two-dimensional model, there exists three longitudinal waves namely Longitudinal wave (P-wave), thermal wave (T- wave), mass diffusion wave (MD-wave) and a set of coupled transverse waves (SV1 and SV2 waves). The phase velocity, attenuation coefficient, specific loss and penetration depth are computed numerically and presented graphically. The fundamental solution for the system of differential equations for steady oscillations in terms of elementary functions has been constructed. Some properties of fundamental solution are also established. Various particular cases of interest are also deduced from the present investigations and compared with the known results.