First described by Klemperer and Rabin in 1931, solitary fibrous tumour of the pleura (SFTP) is a mesenchymal tumour that tends to involve the pleura, although it has also been described in other thoracic areas (mediastinum, pericardium and pulmonary parenchyma) and in extrathoracic sites (meninges, epiglottis, salivary glands, thyroid, kidneys and breast). SFTP usually presents as a peripheral mass abutting the pleural surface, to which it is attached by a broad base or, more frequently, by a pedicle that allows it to be mobile within the pleural cavity. A precise preoperative diagnosis can be arrived at with a cutting-needle biopsy, although most cases are diagnosed with postoperative histology and immunohistochemical analysis of the dissected sample. SFTP, owing to its large size or unusual locations (paraspinal, para-mediastinal, intra-fissural and intraparenchymal), can pose interpretation problems or, indeed, point towards a diagnosis of diseases of a totally different nature. We present some unusual radiographic and computed tomography (CT) images of large SFTP or SFTP located in atypical thoracic locations in patients who underwent surgical resection.