In this lesson, the initial and boundary value problem in Continuum Mechanics will be discussed. Generally, the governing equation is put, and then the initial and boundary conditions are put. The problems that will be solved are finding mass density, finding displacement field for problems of solid mechanics, and generally, the velocity field is used for fluids. Governing equations are written for fluids and solids. Boundary conditions and then the initial conditions are introduced for solids and fluids.