Computational methods for protein structure prediction allow us to determine a three-dimensional structure of a protein based on its pure amino acid sequence. These methods are a very important alternative to costly and slow experimental methods, like X-ray crystallography or Nuclear Magnetic Resonance. However, conventional calculations of protein structure are time-consuming and require ample computational resources, especially when carried out with the use of ab initio methods that rely on physical forces and interactions between atoms in a protein.Fortunately, at the present stage of the development of computer science, such huge computational resources are available from public cloud providers on a payas-you-go basis. We have designed and developed a scalable and extensible system, called Cloud4PSP, which enables predictions of 3D protein structures in the Microsoft Azure commercial cloud. The system makes use of the Warecki-Znamirowski method as a sample procedure for protein structure prediction, and this prediction method was used to test the scalability of the system. The results of the efficiency tests performed proved good acceleration of predictions when scaling the system vertically and horizontally. In the paper, we show the system architecture that allowed us to achieve such good results, the Cloud4PSP processing model, and the results of the scalability tests. At the end of the paper, we try to answer which of the scaling techniques, scaling out or scaling up, is better for solving such computational problems with the use of Cloud computing.