The Russian 1370 Al-Mg-Si-Cu alloy (analogue of 6056) is an advanced material for the skin and stringers of fuselage. However, these alloys are susceptible to the intercrystalline corrosion depending on the heat treatment regimes. The investigations of the effect of heating temperature during the solid solution treatment (530-555)°C and quenching rate, ageing regimes and interval between the quenching and ageing on the structure and properties of 1370 alloy sheets were performed. The strengthening β (Mg2Si) -phase and Q (Al5Cu2Mg8Si6) -phase relationship dependence of the alloy properties is established. Using the dark field electron microscopy which permits to intensify separate diffraction reflexes of strengthening phases the structure of Q-phase precipitates has been studied. Optimization of heat treatment of 1370 alloy sheets provided the combination of fracture toughness characteristic (Kco= 100 MPa√m) high level, the ultimate strength of 400-420 MPa and intercrystalline corrosion no more 100 μm in depth.