A stress control design protocol was developed to minimize coal mine bumps, which are the explosive failure of highly stressed pillars. The protocol was developed for room-and-pillar retreat mining conducted with available continuous miner technology. The inability of existing coal pillar equations to accurately represent the wide total extraction pillars required, forced the development of the pseudoductile coal pillar strength model. A confined pillar core is assumed to reach a maximum stress when surrounded by a yielded perimeter. The width of the yielded perimeter is assumed to increase linearly with increased coalbed thickness. The pseudoductile model was employed in the development of supercritical and subcritical width section design criteria. The supercritical design procedure assumes an infinitely long pillar line, composed of uniformly sized pillars, extracted against an infinitely wide gob area. Tributary area theory was combined with a linear shear angle concept to estimate the loads applied to total extraction pillars adjacent to gob areas. The boundary element code MULSIM/NL was utilized in the development and implementation of a systematic subcritical design procedure to apply the stress shield concept to retreat room-and-pillar coal mining, under bump hazard. The complex distribution of gob side abutment load between the side abutment pillars and the chain pillars in the total extraction zone made computer simulation a necessity. Section layouts were determined for the mining of a 6 ft thick coalbed under overburden up to 2,200 ft thick. The sections consist of total extraction areas separated by continuous abutment pillars. A spreadsheet program LAYOUT was created to summarize and provide for efficient utilization of the bump control design protocol. Based on overburden thickness, coalbed thickness, abutment load linear shear angle, and pillar dimensions entered by the user, LAYOUT calculates a stability factor for the first and second pillar row outbye the expanding gob for supercritical width sections. If the overburden and coalbed thickness conditions do not allow a supercritical section design, LAYOUT develops a subcritical design. / Ph. D.