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.