We study air entrainment by a solid plate plunging into a viscous liquid, theoretically and numerically. At dimensionless speeds Ca = Uη/γ of order unity, a near-cusp forms due to the contact line. The radius of curvature of the cusp’s tip scales by the slip length multiplied by an exponential of -Ca. The pressure from the air flow drawn inside the cusp leads to a bifurcation, at which air is entrained, i.e. there is ‘wetting failure’.