Propagation of the unbounded bright spatial soliton in non-Kerr type media is studied. Numerical calculation results show that propagation of the unbounded bright spatial soliton can take place in the so-called cubic-quintic nonlinear medium. The stability of propagation depends on the values of the asymptotic wave number of the background plane wave q, and of χ(3), χ(5), where the nontrivial phase variation also plays an important role.