Moving to Buenos Aires at a young age, Tinayre directed some 23 films between 1934 and 1974, directing films such as the 1947 thriller A sangre fría (In Cold Blood) which starred actors such as Amelia Bence and Tito Alonso. He was also an acclaimed screenwriter and producer simultaneously contributing in these areas to the films he directed in Argentine cinema.
In 1949 he directed Dance of Fire, which was later entered into the 1951 Cannes Film Festival. His 1960 film La patota was entered into the 11th Berlin International Film Festival. His 1963 film The Dragonfly Is Not an Insect was entered into the 3rd Moscow International Film Festival.
In 1969 he directed Kuma Ching; his last film was to be La Mary (1974), starring then-couple Susana Giménez and boxer Carlos Monzón.
He died in 1994. His widow was the well-known actress and television host Mirtha Legrand.