Using the method of unidirectional waves, we numerically solve a wave equation that describes the vector propagation of a femtosecond laser pulse of few optical cycles in a uniaxial crystal. Propagation of the pulse in the direction normal to the optical axis is studied. taking into account both the second- and third-order nonlinearity, of the crystal. Conversion efficiency as a function of crystal length, pump intensity and pulse duration is studied. As an example, the propagation of a femtosecond laser pulse of tau = 10 fs duration at lambda = 810 nm in a 12-mum thick LiNbO3 crystal is numerically modeled. (C) 2003 Wiley Periodicals, Inc.