One of the major problems in drilling operations is wellbore instability, which is the inability of a borehole to retain its gauge size after being drilled, due to stress redistribution in subsurface rocks. A Mechanical Earth Model (MEM) helps in characterizing the stress state in rocks and defining the optimum mud-weight window to mitigate formation failure. This paper details the construction and calibration of a one-dimensional (1-D) MEM using available well-log and deviation survey data in a normally faulted oilfield in shallow water, Niger Delta. The field lacks core data typically used in calibrating the rock ultimate compressive strength. Statistical analysis was used to select fitting rock strength correlations for sandstone and shale intervals. The MEM was validated with caliper and drilling events logs. The Mohr-Coulomb shear failure criterion gave the highest mud-weight estimates as the lower bound of the optimum mud-weight window. The MEM successfully explains shear failure – a tight-hole incident – which led to a stuck-pipe incident during drilling operations of another well in the same field.