We consider the problem of constructing nonnegative matrices with prescribed extremal singular values. in particular, given 2n - 1 real numbers or sigma((j))(1) and sigma((j))(j), j = 1,...., n, we construct an n x n nonnegative bidiagonal matrix B and an n x n nonnegative semi-bordered diagonal matrix C, such that sigma((j))(1) and sigma((j))(j) are, respectively, the minimal and the maximal singular values of certain submatrices B-j and C-j of B and C, respectively. By using a singular value perturbation result, we also construct an n x n nonnegative matrix with prescribed singular values sigma(1) >= ... >= sigma(n). (C) 2007 Elsevier Ltd. All rights reserved.