In Spain, Principia was born in 1984 as a successor to Principia Mechanica Ltd, created in London in 1980. In 1985, Principia became an independent Spanish firm of consulting engineers, with the objective of responding to increasing demands from companies both at home and abroad in the area of applied mechanics. The company was named after Sir Isaac Newton's Principia Mathematica Philosophiae Naturalis.

Principia's traditional speciality is the analysis of mechanical and structural problems, particularly those with a dynamic and/or non-linear character, in support of the activities of others. Typical examples are impacts, earthquakes, explosions, vibrations, large deformations, etc. as well as many calculations which simply require a high level of precision and reliability. Increasingly, environmental engineering considerations underlie the motivations of many of those projects. Also there is an increasing demand for forensic engineering services in which post-failure investigations are carried out in order to determine the origin of accidents. Additionally, Principia, as the Spanish agent for SIMULIA, distributes and supports SIMULIA products, being the program Abaqus among them. Abaqus is a general-purpose, finite element code, specially powerful for the solution of non-linear problems.

In general, the problems mentioned above are sufficiently complex and infrequent that it is often impractical to try to solve them internally in the industry in which they occur. Principia maintains a high degree of specialisation in order to be able to optimise the solution of such problems for their clients. Working along these lines, the company has maintained considerable activity over the years in relation with the nuclear, civil engineering, petrochemical, defense/aerospace and manufacturing industries. Besides collaborating with Spanish companies, Principia works from Spain for companies and organizations in other countries, primarily in the developed world.