The effect of arbitrary shapes of the two fluid interface on Richtmyer-Meshkov (RM) instability is investigated. It is seen that deviation from sinusoidality in the geometrical shapes has interesting influence on the overall growth rate. In the linear theoretic domain the RM instability may be actually reduced for suitable geometrical shape of the interface. The figures given demonstrate this aspect. This result is important in designing ICF target and also gives an idea to tailor laser pulse for optimum stability of RM modes.