This paper presents theoretical investigation on the cross correlation between torsional vibration ($u_{ heta}$) and translation vibration ($u_x$) of asymmetrical structure under white noise excitation. The formula reveals that the cross correlation coefficient (${ ho}$) is a function of uncoupled frequency ratio (${Omega}={omega}_{ heta}/{omega}_x$), eccentricity, and damping ratio (${xi}$). Simulations involving acceleration records from fifteen different earthquakes show correlation coefficients results similar to the theoretical correlation coefficients. The uncoupled frequency ratio is the dominating parameter to ${ ho}$; generally, ${ ho}$ is positive for ${omega}_{ heta}/{omega}_x$ > 1.0, negative for ${omega}_{ heta}/{omega}_x$ < 1.0, and close to zero for ${omega}_{ heta}/{omega}_x$ = 1.0. When the eccentricity or damping ratio increases, ${ ho}$ increases moderately for small ${Omega}$ (< 1.0) only. The relation among $u_x$, $u_{ heta}$ and corner displacement are best presented by ${ ho}$; a simple way to hand-calculate the theoretical dynamic corner displacements from $u_x$, $u_{ heta}$ and ${ ho}$ is proposed as an alternative to dynamic analysis.