This is a modern textbook for courses in continuum mechanics‎.‎ It provides both the theoretical framework and the numerical methods required to model the behaviour of continuous materials‎.‎ This self‎-contained textbook is tailored for advanced undergraduate or first‎-year graduate students with numerous step‎-by‎-step derivations and worked‎-out examples‎.‎ The author presents both the general continuum theory and the mathematics needed to apply it in practice‎.‎ The derivation of constitutive models for ideal gases‎,‎ fluids‎,‎ solids and biological materials‎,‎ and the numerical methods required to solve the resulting differential equations‎,‎ are also detailed‎.‎ Specifically‎,‎ the text presents the theory and numerical implementation for the finite difference and the finite element methods in the Matlab‎(‎R‎)‎ programming language‎.‎ It includes thirteen detailed Matlab‎(‎R‎)‎ programs illustrating how constitutive models are used in practice‎.‎