This paper investigates the correlation between ground motion parameters and displacement demands of mid-rise RC frame buildings on soft soils considering the soil-structure interaction. The mid-rise RC buildings are represented by using 5, 8, 10, 13, and 15-storey frame building models with no structural irregularity. A total of 105 3D nonlinear time history analyses were carried out for 21 acceleration records and 5 different building models. The roof drift ratio (RDR) obtained as inelastic displacement demands at roof level normalized by the building height is used for demand measure, while 20 ground motion parameters were used as intensity measure. The outcomes show velocity related parameters such as Housner Intensity (HI), Root Mean Square of Velocity (V_rms), Velocity Spectrum Intensity (VSI) and Peak Ground Velocity (PGV), which reflect inelastic displacement demands of mid-rise buildings as a damage indicator on soft soil deposit reasonably well. HI is the leading parameter with the strongest correlation. However, acceleration and displacement related parameters exhibit poor correlation. This study proposed new combined multiple ground motion parameter equations to reflect the damage potential better than a single ground motion parameter. The use of combined multiple parameters can be effective in determining seismic damages by improving the scatter by at least 24% compared to the use of a single parameter.