This paper provides a set of uniform consistency results with rates for non- parametric density and regression estimators smoothed by the beta kernel hav- ing support on the unit interval. Weak and strong uniform convergence is ex- plored on the basis of expanding compact sets and general sequences of smooth- ing parameters. The results in this paper are useful for asymptotic analysis of two-step semiparametric estimation using a first-step kernel estimate as a plug-in.