In this paper, properties of stationary waves of the transverse magnetic (TM) type which have two electric field components, i.e., axial and transverse ones, in a nonlinear self‐focusing medium are discussed. Waves of the TM type are categorized into a solitary wave and several types of waves oscillating in the transverse plane. Analytical expressions of oscillating waves are obtained by using an asymptotic expansion and its extension for the large nonlinearity as well as the small one of the medium. A solitary wave is also discussed numerically, and some differences between the solitary waves of TE and TM types are mentione