is satisfied. The static configuration of radius a 0 has the following density and pressures In what follows we shall study small radial perturbations around the radius of equilibrium a 0 . To this end we adapt a linear relation between p and σ as [7] Here since we are interested in the wormholes which are supported by normal matter, β 2 is the speed of sound. By virtue of Eq.s (19) and (22) we find the energy density in the form This, together with (16) lead us to the equation of motion for the radius of the throat, which reads After some manipulation this can be cast into where in which the functions A and B are We notice that V ( a ) , and more tediously V $^{′}$( a ) , both vanish at a = a 0 . The stability requirement for equilibrium reduces therefore to the determination of V $^{′′}$( a 0 ) > 0 , and it is needless to add that, V ( a ) is complicated enough for an immediate analytical result. For this reason we shall proceed through numerical calculation to see whether stability regions/ 6 σ 0 = − √ f ( a 0 ) 4 π [ 3 a 0 − 4 α a 3 0 ( f ( a 0 ) − 3) ] , (20) p 0 = f ( a 0 ) 4 π [ 2 a 0 + f $^{′}$( a 0 ) 2 f ( a 0 ) − 2 α a 2 0 f $^{′}$( a 0 ) f ( a 0 ) ( f ( a 0 ) − 1) ] . (21) p = p 0 + β $^{2}$( σ − σ 0 ) . (22) − √ f ( a ) + ˙ a 2 4 π [ 3 a − 4 α a 3 ( f ( a ) − 3 − 2˙ a $^{2}$) ] = ( σ 0+ p 0 β 2 + 1 ) ( a 0 a ) 3 ( β $^{2}$+1 ) + β $^{2}$σ 0 $_{−}$p 0 β 2 + 1 . (24) ˙ a 2 + V ( a ) = 0 , (25) A = πa 3 4 α [( σ 0+ p 0 β 2 + 1 ) ( a 0 a ) 3 ( β $^{2}$+1 ) + β $^{2}$σ 0 $_{−}$p 0 β 2 + 1 ] , (27) B = a 2 8 α + 1 − f ( a 2 . (28) σ ( a ) = ( σ 0+ p 0 β 2 + 1 ) ( a 0 a ) 3 ( β $^{2}$+1 ) + β $^{2}$σ 0 $_{−}$p 0 β 2 + 1 . (23) V ( a ) = f ( a ) − ( [ √$_{A}$ 2 + B 3 − A ] 1 / 3 − B [ √$_{A}$ 2 + B 3 − A ] 1 / 3 ) 2 (26) A and B are