Rational schemes for shape preservation of monotone data both in 2D and 3D setups have been developed. $C^1$ rational cubic and partially blended bicubic functions are employed for this purpose. Monotonicity is achieved by extracting constraints on parameters involved in the description of these rational functions. Monotone curves and surfaces have been obtained, which provide evidence that the algorithm used fits most types of monotone data and produces visually pleasing results.