To fill the existing literature gap, the numerical solutions for the oblique stagnation-point flow of Cu-Al2O3/H2O hybrid nanofluid past a shrinking surface are computed and analyzed. The computation, using similarity transformation and bvp4c solver, results in dual solutions. Stability analysis then shows that the first solution is stable with positive smallest eigenvalues. Besides that, the addition of Al2O3 nanoparticles into the Cu-H2O nanofluid is found to reduce the skin friction coefficient by 37.753% while enhances the local Nusselt number by 4.798%. The increase in the shrinking parameter reduces the velocity profile but increases the temperature profile of the hybrid nanofluid. Meanwhile, the increase in the free parameter related to the shear flow reduces the oblique flow skin friction.