Context. Cold dark matter inhomogeneities are considered in a homogeneous background of matter, radiation, and the cosmological constant in a flat universe. Aims. We investigate the influence of the cosmological constant on the non-linear collapse of cold dark matter clusters. Methods. For simplicity, a spherical infall model has been used to describe the collapse of non-relativistic mass shells; besides, an average distribution of density around a cluster of galaxies has been taken. We have found that there is a limit to the mass of the average cluster, which is able to virialize; its value is {M VIR } MAX = 8.1 × 10 14 M . As expected, we found that shells present null proper acceleration at redshift values that are smaller than 0.755. Conclusions. We have noticed that the cosmological constant imposes an upper limit for the mass enclosed by shells, which are able to reach zero proper velocity. Hence, this mass is the maximum mass of the virialized core, {M VIR } MAX . For the average cluster addressed in this work, the value is 2.34 times the mass of the virialized core at present. Shells enclosing masses M > {M VIR } MAX achieve zero proper acceleration and speed up, moving away from the virialized core, and never reach a turn-around point. Shells with M {M VIR } MAX show zero proper aceleration at redshifts close to that at which the universe background acceleration is null. Finally, we have found that the relation between shell proper velocities and their radii can be adjusted by a straight line at z = 0 and from approximately 20 up to 40 Mpc; however, this line does not intercept the origin as velocities due to the Hubble flux do.