This paper presents results of a parametric study of seismic induced lateral-torsional-pounding responses of an asymmetric and a symmetric one-storey system subjected to bi-directional ground motion. The properties of the symmetric model are fixed, while the vibration frequency and eccentricity of the asymmetric model vary in the numerical computation. 20 sets of bi-directional horizontal earthquake ground motion time histories are numerically simulated for the analysis. All the simulated motions are compatible individually with the Newmark-Hall design response spectrum with 5% damping and normalized to 0.5g. Ensemble mean peak responses of the two systems to the 20 sets ground motions are estimated. Both linear elastic and nonlinear inelastic behaviours are studied. Effects of torsional stiffness, structural vibration frequency, eccentricities, and initial gap between two structures are investigated. Numerical results are presented in dimensionless form and compared with the code torsional provisions. In this paper, the input ground motion time histories at all the structural supports are assumed to be uniform. An accompany paper of this study is devoted to discuss the effect of the spatially varying ground motion on coupled lateral-torsional-pounding responses of the adjacent structures (Hao and Gong 2005).