The first detailed measurement of the dependence oil target nuclear mass of the average Squared transverse momentum < p(t)(2)> of pi(+), pi(-), and K(+) mesons from deep-inelastic lepton scattering is obtained as a function of several kinematic variables. The data were accumulated at the HERMES experiment at DESY, in which the HERA 27.6 GeV lepton beam was scattered off several nuclear gas targets. The average squared transverse momentum was clearly observed to increase with atomic mass number. The effect increases as a function of Q(2) and x and remains constant as a function of both the virtual photon energy v and the fractional hadron energy z, except that it vanishes as z approaches unity. (C) 2010 Elsevier B.V. All rights reserved.