Joseph Armstrong (born Bewcastle, Cumberland, 21 September 1816, died Matlock Bath 5 June 1877) was an English locomotive engineer and the second locomotive superintendent of the Great Western Railway. His younger brother George and one of his sons ("Young Joe") also became outstanding engineers in the employment of the GWR.

After a spell in Canada, in 1824 Joseph's family took up residence in Newburn-on-Tyne, where his father Thomas became a bailiff to the Duke of Northumberland. Joseph attended Bruce's School in Newcastle, where Robert Stephenson had also been a pupil. In 1823 Robert Stephenson, in collaboration with his father George, had set up his locomotive works in the city. Moreover, Newburn was at one end of the Wylam Waggonway, where the sight of the famous locomotives Puffing Billy and Wylam Dilly must have inspired young Joseph's enthusiasm as an engineer. Newburn also had colliery railways worked by stationary engines, and it was at one of these, Walbottle Colliery, that Armstrong found his first employment.

As well as their acquaintance with the Stephensons, an important contact for the Armstrongs was the Methodist philanthropist Timothy Hackworth, who in 1825 became first locomotive superintendent of the brand-new Stockton and Darlington Railway. Through Hackworth, the teenage Armstrong may have gained experience driving locomotives on the Stockton and Darlington, and it has been suggested that Hackworth was probably a strong influence on his notably humane religious and social outlook when later in a position of great responsibility at Swindon Works on the Great Western.

Meanwhile, continuing to gain hands-on experience with the pioneering steam locomotives of the time, at the age of 20 (1836) Armstrong was employed by Edward Woods as a driver on Stephenson's Liverpool and Manchester Railway, moving four years later to a similar post on the Hull and Selby Railway, where he was promoted to the post of foreman and became acquainted with the forward-looking locomotive designs of John Gray. On following Gray to Brighton Works in 1845, Armstrong also got to know another pioneering locomotive engineer of the period, David Joy.

In 1847 Armstrong was appointed assistant locomotive superintendent to Edward Jeffreys, on the Shrewsbury and Chester Railway (S&CR), whose repair works was at Saltney. When Jeffreys left in April 1853, Armstrong was promoted to Locomotive Superintendent. Also in 1853, the S&CR pooled its locomotives with the Shrewsbury and Birmingham Railway (S&BR), and Armstrong became responsible for the combined fleet, moving to the ex-S&BR repair shops close to Wolverhampton (High Level) station, where he appointed his younger brother, George as his assistant and works manager.

On 1 September 1854, the S&CR and S&BR amalgamated with the Great Western Railway (GWR), whose locomotive workshops were at Swindon. The two smaller railways became the newly established Northern Division of the GWR. Armstrong remained in his position (although he now reported to Daniel Gooch, who was based at Paddington), and a larger works was established at Wolverhampton to replace the former S&BR premises.

The ex-S&CR and ex-S&BR locomotives were the first standard-gauge locomotives to be owned by the GWR. All these had been supplied by independent locomotive manufacturers, but the GWR Board wished to have future standard-gauge locomotives built at Wolverhampton. Since Wolverhampton was not yet equipped for new construction, Swindon began building standard-gauge locomotives in 1855, which were to the designs of Gooch; some of these were built by outside manufacturers. In 1859, Wolverhampton also began building locomotives, to the designs of Armstrong, who had been given a certain degree of autonomy.

In 1864, Gooch resigned the post of Superintendent of Locomotive Engines, and Armstrong was promoted to replace him; in addition to Gooch's locomotive duties, Armstrong was also made responsible for carriages and wagons, which was reflected in his new job title, that of Locomotive, Carriage and Wagon Superintendent. As with Gooch, his responsibilities encompassed the Northern Division, which he was happy to devolve to his younger brother, George.