Protein compressibility is believed to be one of the factors determining the functional properties of a protein. We study the relation between the three-dimensional structures of proteins and their compressibility [1]. By applying persistent homology to the function defined as the Euclidean distance from the molecule, we could estimate the sizes of cavities and tunnels in the protein molecule. The sizes of these features are suspected to be correlated with compressibility. It turns out to be a ratio between the number of cavities and tunnels of specific sizes that influences the compressibility of the protein.