A adhesive sheet or film placed in contact with a surface network formed by the edges of the cell walls of a honeycomb core panel is reticulated and conformed to the shape of the surface network to form a bead of adhesive on the surface network and the contiguous portions of the cell walls without depositing excess adhesive onto the interior cell walls. A method for reticulating the adhesive includes the steps of (a) contacting the surface network of a honeycomb core panel with a continuous film of adhesive material, (b) heating the film overlying at least a portion of the surface network to cause the heated portion of the adhesive film to adhere to the surface network and to reduce the cohesive strength of the heated portion of the adhesive film covering the honeycomb cells, and (c) thereafter injecting a pressurized gas through the cells of the honeycomb core toward the heated portion of the adhesive film, causing the heated portion of the film covering each of the honeycomb cells to distend outwardly away from the surface of the honeycomb core and to rupture. The surface tension of the heated adhesive film causes the ruptured portions of the film to contract toward the surface network leaving a bead of adhesive covering the surface network and the portion of the honeycomb cell walls contiguous to the surface network.