A Co20.5Ni40.5Fe39 magnetic film was electrodeposited onto a copper wire 50 µm in diameter. The magnetoimpedance (MI) effect, (ΔZ/Z)H(%) = ((Z(H) − Zmax)/Zmax) × 100, was measured in the Co20.5Ni40.5Fe39/Cu composite wire under varying tensile stresses up to 30 MPa. The results showed that large MI and stress impedance (SI) effects can be observed in the Co20.5Ni40.5Fe39/Cu composite wire. The MI curve at zero tensile stress shows a small split peak in the low-field region. With increasing applied tensile stress, single-peak behaviour of the MI effect is observed. The magnitude of the MI and SI effects decreases with increasing tensile stress, σ. The peak values of (ΔZ/Z)H(%) for the sample decrease from 265% at σ = 0 to 39% at σ = 30 MPa at 40 kHz ac driving-current frequency. The impedance of a sample under the effect of 25 MPa tensile stress at 40 kHz ac driving-current frequency showed variations of about 146%. It was also found that the frequency value, f*, where the maximum MI effect was observed as a function of driving-current frequency, increases with increasing tensile stress.