We present a spectroscopic and photometric study of the Double Period Variable HD 170582. Based on the study of the ASAS V-band light curve we determine an improved orbital period of 16.87177 ± 0.02084 days and a long period of 587 days. We disentangled the light curve into an orbital part, determining ephemerides and revealing orbital ellipsoidal variability with unequal maxima, and a long cycle, showing quasi-sinusoidal changes with amplitude ∆V= 0.1 mag. Assuming synchronous rotation for the cool stellar component and semi-detached configuration we find a cool evolved star of M 2 = 1.9 ± 0.1 M , T 2 = 8000 ± 100 K and R 2 = 15.6 ± 0.2 R , and an early B-type dwarf of M 1 = 9.0 ± 0.2 M . The B-type star is surrounded by a geometrically and optically thick accretion disc of radial extension 20.8 ± 0.3 R contributing about 35% to the system luminosity at the V band. Two extended regions located at opposite sides of the disc rim, and hotter than the disc by 67% and 46%, fit the light curve asymmetries. The system is seen under inclination 67.4 ± 0.4 degree and it is found at a distance of 238 ± 10 pc. Specially interesting is the double line nature of He i 5875; two absorption components move in anti-phase during the orbital cycle; they can be associated with the shock regions revealed by the photometry. The radial velocity of one of the He i 5875 components closely follows the donor radial velocity, suggesting that the line is formed in a wind emerging near the stream-disc interacting region.