Recently, many works on computer simulations (mainly, particle simulations) of relativistic laser-plasma interactions have been done energetically, and the formation of electromagnetic solitary pulses has been also reported. In this paper, we study fluid simulations on relativistic laser-plasma interactions and demonstrate the generation of electromagnetic subcycle pulses due to the nonlinear effect. The simulation is one-dimensional, where the Maxwell and fluid equations of the electron and ion are solved numerically for cold plasma. The fluid equation of the electron is fully nonlinear and the relativistic effects are taken into account, on the other hand, that of the ion is linearized because the ion response is very slow due to the large ion-to-electron mass ratio. For stationary propagation of laser pulses with circular polarization, we obtain a nonlinear wave equation for a laser pulse coupled with an equation for electrostatic wave component, and solve numerically those equations to obtain a subcycle pulse solution. We obtain moving subcycle pulses and it is shown that the pulse width becomes shorter for the larger wave amplitude. In the fluid simulations, an incident laser pulse with linear or circular polarization is launched into plasma. The incident laser pulse is decomposed into an extremely-short pulse and the bulk of the laser pulse due to the nonlinear effect in plasma. The FWHM of the pulse is found to be smaller than one carrier wavelength of the incident laser pulse, and the excited pulse is sub-cyclic. The bulk of the laser pulse is gradually expanding due to the effect of plasma dispersion, on the other hand, the subcycle pulse is seemed to be propagating with preserving its waveform. The excited subcyle pulse with linear polarization is faster than that with circular polarization. It is also found that the strong electrostatic wake field is also excited and follows behind the subcyle pulse.