The penetration of a viscous lubricant into a two dimensional surface crack under a rolling contact stress was calculated. The finite element method was applied to solve the Reynolds equation coupled with the elastic deformation of the crack. The lubricant begins to flow into the crack when the contact pressure is passing the crack mouth. The lubricant enters to the crack tip and increases the stress intensity factor, when a nondimensional parameter β=ηνE2/(ap30) is small. The crack does not open when β is large, because the contact pressure has passed before the lubricant flows into crack. The critical values of β were calculated. The penetration of the lubricant becomes easy when a frictional stress acts as the crack opening.