24 March – Two 18-year-old men and a 19-year-old man attempt to disrupt the official opening of Sydney's new Circular Quay overhead roadway.[7] Two of the men are armed with gardening shears and the other carrying a roll of toilet paper as they jump a railing and rush towards a party of dignitaries as New South Wales premier Joseph Cahill prepares to cut the ribbon.[7] Before the men could reach the ribbon, police officers tackled the men who were later taken to the Phillip Street police station where all three are charged with offensive behaviour, while two of the men are charged with carrying a cutting instrument.[7] During a speech, Cahill states that the new roadway was indicative of Sydney's growth and said he believed the new road would greatly relieve inner city traffic congestion although there was much more to be done to solve Sydney's traffic issues.[7] The road ultimately becomes known as the Cahill Expressway after lord mayor Harry Jensen successfully proposes in August 1958 that the road should be named in Cahill's honour.[8]
26 March – Leader of the Country Party, Sir Arthur Fadden formally announces his resignation as the party's leader before Minister for Trade John McEwen is unanimously elected as his successor.[9]
Gary David Matthews, an 18-year-old gunner with the 111th Light Anti-Aircraft Battery appears in North Sydney Court of Petty Sessions charged with raping and assaulting with intent to murdering 39-year-old Victoria Joan Hawkins, wife of a British Army Major at Middle Head Army Barracks the previous day.[15][16] The charge of attempted murder is subsequently dismissed the following month when the solder is committed to stand trial.[17] Despite pleading not guilty to the charge, Matthews is found guilty in the Central Criminal Court of raping Hawkins and is sentenced to 12 years imprisonment.[18]
11 April – 14-year-old student Margaret Eleanor Thomas is kidnapped by a man who broke into from Burwood Methodist Ladies College in Sydney.[20][21] The girl's body is found a short time later in Queen Elizabeth Park in Concord.[20][21] 29-year-old labourer John Charles Smith is charged with her murder.[22] He is also charged with having broken into a house in Burwood on 11 February 1958 and raping and inflicted grievous bodily harm on a 13-year-old girl.[23] Smith pleads not guilty to Thomas' murder, but after a four-day trial in June 1958, he is found guilty in the Central Criminal Court and is sentenced to penal servitude for life.[21]
21 December – A 16-year-old boy is rescued after falling into the sea from a 150 ft cliff at Torquay and washed into a small cave at the base of the cliff.[35] During the rescue, the boy falls from the stretcher and is washed out to see when two of the lifesavers fall into a hole, with one of the men swimming out to again retrieve the boy.[35] The boy was taken to Geelong Hospital and was discharged the following day suffering only abrasions and bruises.[35]
2 March – Sydney radio station 2UE publishes Australia's first ever Top 40 music chart.[37]
2 April – Patrick White is announced as the inaugural Miles Franklin Award winner, awarded the prize for his novel Voss.[38] The award is presented to White by prime minister Robert Menzies who described the novel as a "quite remarkable work".[38]
21 May – Postmaster-General Charles Davidson officially opens ABV-2's new television studios in the Melbourne suburb of Ripponlea with the Australian Broadcasting Commission pledging that their new facilities in Melbourne will provide new opportunities for Australian artists, writers and composers.[43]
^Hastings Deering, Harold (15 January 1958). "Faith in the future". The Sydney Morning Herald. p. 4. Retrieved 10 April 2025.
^"Qantas plans outlay of £7million at Mascot by 1960". The Sydney Morning Herald. 15 January 1958. p. 5. Retrieved 10 April 2025. He was speaking at the official departure from Mascot of Qantas' first commercial 'round-the-world' service.
^"Flashback to 1958 in the Great Lakes". Great Lakes Advocate. 27 April 2018. Retrieved 10 April 2025. On September 30, 1958 the ANZAC Day Act 1958 received royal assent, making Anzac Day a national public holiday in Australia
^Arneil, Chris (2018). "The Top 40 transformed Australian radio". National Sound and Film Archive. Retrieved 13 April 2025. Top 40 radio began on Sunday 2 March 1958 when 2UE began playing and promoting the format as a daily feature, accompanied by the issuing of a weekly chart