The state of matter called a solid does have a definite volume and shape. This is one of the properties that defines a solid. Some other properties pertaining to a solid are that the molecules within a solid are packed tightly, which affects the solid's compressibility.
Solids cannot be compressed as easily as a gas. Solids are more rigid than either gases and liquids, which are two other states of matter.
Some properties of these two states of matter are that gases do not have either a fixed volume or shape, while liquids can conform to the shape of the container it is in. Although they can assume the shape of a container, the volume of liquids remains constant. For example, if a person pours 10 milliliters of water first into a square container and then into a circular one, the shapes may change but the volume of water is still the same. Gases and liquids can flow freely, but this is not the case for solids.