The second generation Ford Thunderbird (also called Square Bird) was produced by Ford for the 1958 to 1960 model years as a successor to the popular 1955–1957 two-seater. In response to Ford-conducted surveys two major changes were made to attract potential buyers: two rear seats were added and the level of luxury and features of a full-sized car were incorporated into a mid-size platform.

As a result, sales soared and the new model dramatically expanded the personal luxury car market, winning the Motor Trend Car of the Year in 1958. Sales totalled 198,191 over three model years, approximately four times that of the earlier two seat model.

Along with the 1958 Lincolns, the 1958 Thunderbird was the first Ford Motor Company vehicle designed with unibody construction.

Although the 1955–1957 Ford Thunderbird had proved successful (in comparison to the Chevrolet Corvette), Ford executives—particularly Robert McNamara—still felt its overall sales volume had room to improve. Market research suggested sales of the Thunderbird were limited by its two-seat configuration, making it unsuitable for families. The Studebaker Speedster and the Chrysler 300C shared many appearances with the Thunderbird, while offering a rear seat. As a response, Ford executives decided to add a rear seat to the Thunderbird. The listed retail price was US$3,408 for the base price ($38,154 in 2024 dollars ). Mercury also saw the introduction of a flagship hardtop coupe with a similar approach to luxury called the Mercury Turnpike Cruiser with a longer wheelbase and two inches more for width dimensions, then updated to the 1958 Mercury Park Lane.

The new Thunderbird had a distinct new styling theme. The styling department drove the design entirely and approved it before the engineering was considered. The design was one of two proposals, styled primarily by Joe Oros, who later worked on the 1964 Ford Mustang. However, the losing proposal, styled by Elwood Engel, would gain its own place in Ford Motor Company history: after minor revisions, it would become the 1961 Lincoln Continental.

The four-seat Thunderbird was designed with unibody construction, eschewing a separate chassis shared with the all-new Lincoln built at the all new factory in Wixom, Michigan. The intent was to allow the maximum interior space in a relatively small exterior package. The 1958 Thunderbird was only 52.5 inches tall, nearly 9 inches shorter than an average American sedan; the Thunderbird had only 5.8 inches of ground clearance. Ford incorporated the higher drivetrain tunnel that was required in a lower car into a center console dividing both front and rear seats which featured ashtrays, switches, and minor controls.

The remainder of the engineering was conventional, with Ford's new 300-hp 352 cu in (5.8 L) FE-series V8 coupled to a three-speed manual transmission, with overdrive or Cruise-O-Matic three-speed automatic transmission optional, and all were steering column installed gear selection. Front suspension was independent, with coil springs and unequal-length A-arms. The rear was initially a live axle suspended by trailing arms and coil springs, which were intended to be interchangeable with optional air springs that were canceled before production. This was changed to a more conventional leaf spring suspension in the 1959 model year. Drum brakes were used on all four wheels.

Various delays conspired to have production start only on December 20, 1957, much later than the normal start expected in September; the 1957 Thunderbird was thus built for three extra months.