This thesis presents basic attenuation relationships for the maximum incremental velocity,MIV, of earthquake ground motion records. Multiple regression analyses are conducted to determine relationships between the MIV and the relevant earthquake parameters, such as magnitude, distance, soil conditions, and fault type. The PEER-NGA (2009) strong ground motion database is expanded for the purposes of the study, to include the 'orientation-independent' geometric mean MIV of the two orthogonal horizontal components of a given record. The proposed attenuation relationship can be used to estimate the MIV at a given site, similar to currently available models for other ground motion intensity parameters such as the peak ground acceleration (PGA) and velocity (PGV), as well as spectral acceleration (SA) and velocity (SV).