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 16.871 77 +/- 0.020 84 d and a long period of 587 d. 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 Delta V=0.1 mag. Assuming synchronous rotation for the cool stellar component and semidetached configuration we find a cool evolved star of M-2 = 1.9 +/- 0.1 M-circle dot, T-2 = 8000 +/- 100K and R-2 = 15.6 +/- 0.2 R-circle dot, and an early B-type dwarf of M-1 = 9.0 +/- 0.2 M-circle dot. The B-type star is surrounded by a geometrically and optically thick accretion disc of radial extension 20.8 +/- 0.3 R-circle dot contributing about 35 per cent 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 per cent, fit the light-curve asymmetries. The system is seen under inclination 67.degrees 4 +/- 0.degrees 4 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 antiphase 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.