The aircraft came down just after taking off from Boufarik military airport, west of Algiers.
An inquiry is under way into the cause of the crash – Algeria’s worst-ever air disaster. The government has declared three days of national mourning.
Most of the dead are army personnel and their families, the defence ministry says. Ten crew members also died.
Passengers from Western Sahara, a disputed territory annexed by Morocco after Spain withdrew in 1975, were among the fatalities.
The Polisario Front, which is seeking independence for the territory and is backed by Algeria, says 30 Western Saharans, including women and children, died. A senior member of Algeria’s ruling FLN party said those killed included 26 Polisario members.
The plane, an Ilyushin Il-76, was travelling to Bechar and Tindouf in the south-west of the country. The Tindouf region, which borders Western Sahara, is home to refugee camps and serves as a base for the Polisario Front.