This paper presents a simple physical and mathematical model and experimental support of the manner in which magnetic flux penetrates into a high‐field superconductor. Based on this model a new device using high‐field superconductors in their bulk form called a superconducting magnetic flux compressor is proposed. Present theory suggests that magnetic field strengths approaching the critical field strength of a high‐field superconductor (> 100 kOe) should be attainable using the apparatus and techniques described. It was found experimentally with the particular high‐field superconductors tested that compressed field strengths of 15 kOe could be achieved. Beyond this value anomalous magnetic flux jumping occurred that limited the field strengths obtainable. The characteristic conditions under which magnetic flux jumping is found are discussed. The experimental results also suggest that heat is generated when a high‐field superconductor is exposed to an alternating magnetic field well below the critical field strength.