A new solution with constant torsion is derived using the field equations of f(T).Asymptotic forms of energy density,radial and transversal pressures are shown to meet the standard energy conditions,i.e.,weak and null energy conditions according to some restrictions on T0,f(T0) and fT(T0). Other solutions are obtained for vanishing radial pressure and for specific choices of f(T).The physics relevant to the resulting models is discussed.