The mid-century plane, a Junkers JU-52, crashed in the Piz Segnas mountain range, near the Austrian border.
Officials said Sunday the vintage aircraft appeared to hit the ground near-vertically and at a high speed.
"The police have the sad certainty that the 20 people aboard perished", police spokeswoman Anita Senti told a news conference.
A small plane crashed in the Swiss Alps, killing 20 people, according to local officials.
Police said those killed were couples from the Swiss cantons of Zurich, Thurgau, Lucerne, Schwyz, Zug and Vaud, along with a three-member family from Austria and three crew members from Thurgau and Zurich.More news: Google Courts Chinese Market With Censored Search
Almost 5,000 Ju-52 planes, a product of Germany's Junkers, were manufactured between 1932 and 1952.
The area, which includes a glacier, is popular with hikers.
The cause of the crash, which occurred hours after a family of four was killed when their small plane went down further west in the Alps, is under investigation.
A plane crashed on the Piz Segnas mountain. Knecht said that while heat can affect an aircraft's performance, experienced pilots could deal with that.
The German-built Junker JU52 HB-HOT aircraft, dating from 1939 and nickamed "Iron Annie", was a collectors' aircraft. He said it had its full annual service during the winter, and "we know of no technical problems with this aircraft". The JU-Air airline operated three of the vintage planes - decommissioned by the Swiss Air Force and affectionately known as "Auntie Ju" planes - as part of sightseeing tours, Reuters reported.