The effect of bimodularity ratio on free vibration characteristics of cross-ply conical panels of various geometry and lamination scheme is studied. Forced vibration response is also studied for a typical case. The formulation is based on first order shear deformation theory and Bert's constitutive model. An iterative eigenvalue approach is employed to obtain the positive and negative half cycle free vibration frequencies. Galerkin's approach in time domain is used to obtain the frequency response. It is interesting to note that there is a significant difference between positive and negative half cycle frequencies depending on panel parameters. Also, there is a significant difference in positive and negative half cycle forced response amplitudes due to bimodularity.