Laminar film condensation on a vertical plate with an upward vapor flow is studied. An approximate integral model of the condensate film and the boundary layer of the vapor is numerically solved, taking into account both gravity and interfacial shear. Here, three types of solution are examined: (i) zero film thickness at the bottom; (ii) zero flowrate with a finite film thickness at the bottom; and (iii) negative flowrates at the bottom. The film thickness and the average Nusselt number are shown as functions of the distance along the plate and the plate length, respectively. The terminal lengths of the solutions of the types (i) and (ii) are calculated against the degree of the subcooling. Moreover, the results are compared with those derived using the approximation method where the shearing stress on the vapor–liquid interface is composed of only the momentum transferred by the suction mass (the Shekriladze–Gomelauri approach). It is found that the average Nusselt number is well described by the Shekriladze–Gomelauri model in the range of the solution type (ii), while the average Nusselt number for the thinnest-film solution of the type (iii) is asymptotically consistent with the Shekriladze–Gomelauri value for long plates.