The physical, thermal, and mechanical properties of snow, ice, and permafrost, specifically frozen ground, are responsible for the structure and behavior of these cryospheric materials. A fundamental understanding of these properties is therefore key to evaluating associated cryospheric hazards. The material properties of snow, ice, and permafrost vary over many orders of magnitude. Generally, ice has the smallest range in physical and thermal properties (e.g., density or thermal conductivity), while properties of snow and frozen ground have much larger variations. Frozen ground has the largest absolute range in thermal properties, and snow has the largest relative range in physical properties. The mechanical response of each material, including its strength and creep behavior, also varies widely, depending on stress, temperature, and loading rate. Rapid loading under cold conditions results in brittle behavior with high peak strength and small critical strain, whereas slow loading under warm conditions results in ductile behavior with low peak strength and large strain. A full appreciation of the hazards associated with snow, ice, and permafrost requires an understanding of how the basic properties of these cryospheric materials are influenced by environmental conditions.