Let T be a time scale with 0, T epsilon T. We investigate the existence and multiplicity of positive solutions to the nonlinear second- order three- point boundary- value problem u(Delta del)(t) + a(t) f(u(t)) = 0, t epsilon [0, T] subset of T, u(0) = beta u(n) , u(T) = alpha u(n) on time scales T, where 0 < n < T, 0 < alpha < T/n, 0 < beta < T-alpha eta/T-eta are given constants.