A two-stage analysis of the support-rock interaction is carried out using a proposed numerical procedure. The procedure provides a simplified solution for readily obtaining the final support load and rock mass displacement that is easier to use than the conventional Convergence-Confinement Method (CCM). The procedure accounts for the strain-softening behaviour of the rock mass and the effect of delayed support installation. Based on the procedure, a method to determine the delayed distance and allowable displacement for the support installation is presented. A Modified Ground Reaction Curve (MGRC) that relates the rock mass displacement to the final support load is introduced. The effects of the rock mass quality, initial stress, support type and strain-softening, dilatancy behaviours on the delayed distance and allowable displacement are investigated. A comparison between the predictions of the MGRC and GRC is conducted. The results indicate that the influence of the rock mass quality and initial stress on the support-rock interaction is more significant than that of the strain-softening and dilatancy behaviours. An approximate support design using the GRC may be acceptable for a weak rock mass, whereas the GRC results in an overly conservative support design for an excellent rock mass.