Natural gas hydrates (or methane hydrates) could become a major energy source but could also exacerbate global warming, because as the climate warms, hydrate deposits deep under the oceans or in permafrost may release methane into the atmosphere. There are many shallow deposits of gas hydrates in fine-grained muddy sediments on the seafloor. However, the mechanical properties of these sediments have not yet been investigated because of the engineering challenges in coring and testing at in situ temperatures and pressures. Here we present the first uniaxial and triaxial strength and stiffness measurements of pure massive natural gas hydrates and muddy sediments containing hydrate nodules obtained by pressure coring. As a result, we were able to observe the hydrate undergoing a catastrophic brittle failure. Its strength and deformation moduli were 3 and 300 MPa, respectively. Muddy sediments containing hydrate nodules had the same strength as that of hydrate-free sediments.