Abstract The estimation of seismic demand that connects the ground motion intensity measure and the damage measure of structures is one of the most important components in the performance-based design. The random nature of earthquake ground motion with great uncertainties in structural properties has posed challenges before this estimation. In this study, the suitability of different scalar and vector intensity measures of ground motion is quantified by using information theory and relative entropy concepts in the representation of ground motion uncertainty. The multilinear demand models for a better estimation of the seismic demand of structures are developed for near-fault pulse-like and ordinary ground motions, separately. The results indicate that the measures based on the spectral acceleration, velocity, and vector values are more appropriate intensity measures in the low, moderate, and high levels of damage for pulse-like records, respectively. For ordinary records, the use of vector IMs is not recommended due to their complexities and slight superiorities to scalar IMs. If the evaluations require a simple IM in a single-linear demand model for all the damage, the measures of VSI and SIH would be recommended.