Variations in the direction of the maximum horizontal compressive stress (SHmax) may significantly change the potential of faults to slip, especially if the SHmax orientation changes over relatively small distances. To estimate the potential for slip on mapped faults in the Delaware Basin where a regional, large (~150°) SHmax clockwise rotation is observed from north to south, we adapted the Fault Slip Potential (FSP) code (freely available from the Stanford Center for Induced and Triggered Seismicity) to accommodate continuous variations of stress orientation. Using an interpolated and smooth stress field, the upgraded version of the software takes discrete stress orientation values sampled from the smoothed stress field at the center of each specific fault segment for probabilistically determination of fault slip potential. In addition, the new code makes it possible to estimate the slip potential with relation to changes in the relative magnitudes of the three principal stresses by using a discrete Aϕ parameter. We present an updated FSP map of the Delaware basin utilizing the continuous stress orientation map and newly identified basement-rooted faults in the basin. Both the new FSP analysis technique and re-mapping of the faults in the area indicates that the Grisham fault (one of the largest mapped faults in the basin) is less likely to slip in response to fluid pressure increases than previously believed. However, several other basement-rooted faults that are parallel to the SHmax direction may become a seismic hazard if there is deep water disposal in their vicinity.