The two previous elections had resulted in a parliamentary deadlock due to an even number of seats (30) in the House of Assembly. Prior to the 1959 election, the number of seats was increased to 35.
The Australian Labor Party won the most seats in the newly-expanded House of Assembly, but not enough to govern in a majority as two seats were won by Independents. The 1959 election was the last occasion in which an ungrouped independent (Bill Wedd) won a seat in Tasmania.
Former Labor Treasurer Dr Reg Turnbull won two quotas in his own right as an independent in Bass, representing 5.64% of the statewide result.