Abstract: To investigate the stability of bivariate Weibull distribution from the viewpoint of information geometry,the set of all bivariate Weibull distributions was considered as a manifold which was called bivariate Weibull statistical manifold. By computing the Fisher information matrix,the α-connections,α-curvature tensors,α-scalar curvature,and dual geometric structures were obtained. Moreover,bivariate Weibull statistical manifold was dual flat and had constant sectional curvature for α=± 1. Meanwhile,in virtue of the dual flat geometric structures,the instability of the geodesic spreads on this manifold was obtained via the divergence(or instability) of the Jacobi vector field.