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 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=0.1mag. 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_{sun}, T_2=8000+/-100 K and R_2_=15.6+/-0.2 R_{sun}, and an early B-type dwarf of M_1=9.0+/-0.2 M_{sun}. The B-type star is surrounded by a geometrically and optically thick accretion disc of radial extension 20.8+/-0.3 R{sun}_ contributing about 35 percent 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 percent, fit the light-curve asymmetries. The system is seen under inclination 67.4{deg}+/-0.4{deg} and it is found at a distance of 238+/-10 pc. Specially interesting is the double line nature of HeI 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 HeI 5875 components closely follows the donor radial velocity, suggesting that the line is formed in a wind emerging near the stream-disc interacting region.