The propagation characteristics of ultrashort high-power laser pulses through low density plasmas is analyzed by considering relativistic effects. The expresssions of refractive index, electron density, electrostatic field and the dimension of electron cavity are derived. For laser power exceeding the dritical power of self-guiding, self-guiding occurs and laser beam oscillates along the propagation direction. For the laser power exceeding the critical power (P c≈2.5 TW) of the electron cavitation, electron cavity occurs. The expression of the electron cavity dimension is presented. With the laser power increasing, cavity dimensions are almost independent to the laser power, which implies that the electron cavity prevents the further focusing of the laser pulses.