<p>Using a bi-axially stretching surface, this study examines the axisymmetric rotational stagnation-point flow of a micropolar fluid. Similarity transformations are used to transform the governing equations into a nonlinear ordinary differential equations system. Numerical technique, specifically the built-in technique bvp4c in MATLAB, is employed to solve the transformed equations. The results of our analysis reveal that there are dual solutions in certain parameter ranges. We found that increasing the magnitude of <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\beta\)</EquationSource> <EquationSource Format="MATHML"><math> <mi>β</mi> </math></EquationSource> </InlineEquation>, the domain of <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\alpha\)</EquationSource> <EquationSource Format="MATHML"><math> <mi>α</mi> </math></EquationSource> </InlineEquation> decreases where the solution exists. Also, the micropolar fluid parameter <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\kappa\)</EquationSource> <EquationSource Format="MATHML"><math> <mi>κ</mi> </math></EquationSource> </InlineEquation> strongly affects the solution and decreases the domain for <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\alpha\)</EquationSource> <EquationSource Format="MATHML"><math> <mi>α</mi> </math></EquationSource> </InlineEquation> where solution exists. Dual solutions indicate that multiple flow configurations can occur under identical physical conditions, having important implications for the design and analysis of micropolar fluid engineering systems.</p>