This paper computes the conductance of an open ellipse cavity and discusses the effect of finite leads on conductance. The lead introduces mode coupling with bound states in the cavity which contributes to Fano resonant line shapes in conductance. By examining the resonant states in the cavity, the effects of state mixing and annular probability distribution of wave function due to the presence of leads are found. The results have been compared with the transport properties of other systems. The finite leads result in two effects, i.e. the evanescent mode contribution and additional oscillations, to the conductance.