1960 was the first year for Unibody construction, the first year for Chrysler's ram induction system, and the first year for Chrysler's new Slant-Six engine. The original 318 and 383 were available, along with a 361. The 225 cu in (3.69 L) slant-6 produced 145 hp (108 kW) at 4000 rpm. The 383 produced 330 hp (250 kW).
The Fury remained Plymouth's sales volume model through the early 1960s. Tailfins were removed for 1961, leaving the car with unpopular styling. Then Chrysler's president overheard and misunderstood Chevrolet chief Ed Cole saying Chevrolet would not have true full-size cars for 1962.