Analytical study of wave growth on hollow conical liquid sheets was made. By using small wave amplitude model, the linearized perturbation equations of the liquid phase and the gas phase were solved. After some rather tedious algebraic manipulations, the characteristic equations relating the non-dimensional temporal growth rate of a disturbance on conical liquid sheets to the normalized wave numbers were obtained. The numbers are the generalization for the well-known cases of round cylindrical jets and the annular liquid sheets. The characteristic equations are the solid cornerstone of theoretical analysis of conical liquid sheets' atomization.