The short pulse (SP) equation was proposed as a model nonlinear equation describing the propagation of ultra-short optical pulses in nonlinear media [1].Originally, it has stemmed from an attempt to construct integrable differential equations associated with pseudospherical surfaces [2].It is an alternative of the cubic nonlinear Schr(o)dinger (NLS) equation.Although the integrability of the SP equation has been established from various points of view [2-6], only a few results are available about solutions of the equation [7-10].Here we develop a systematic procedure for constructing special solutions of the SP equation which include both periodic and soliton solutions.