This paper proposes the sufficient conditions for positivity preserving cubic boundary curves defined on rectangular grid using a polynomial solution of fourth order linear PDEs in order to improve the positivity preserving of the interpolating surface. We derive a sufficient condition on boundary curves for each edge of bicubic rectangular Bézier patches where the lower bounds of edge Bézier ordinates are adjusted independently. By using two well-known test functions, our result shows that the proposed method is well performed in terms of preserving the positivity of the boundary curves and improves the positivity preserving of overall interpolating surfaces. © 2013 Pushpa Publishing House.