Abstract <p>We study movable singularities of the Blasius equation in the complex plane. Numerical algorithms of their localization are given that allow to find singularities with high accuracy. All these singularities are equivalent and may be represented by one of them. We obtain an asymptotic expansion in the neighborhood of the singularity in explicit form and compute its coefficients. This power-logarithmic expansion is shown to be convergent and giving a local parametrization of the Riemann surface of the Blasius function.</p>