Maslow's theory is by far the most known theory of motivation, and the most common in the business and management practice. Herzberg's theory fits the observations and explains some aspects of human motivation left unexplained by Maslow. However, these theories have never been formalized on a strictly mathematical basis. The present article gives an outline of a mathematical model of theories of motivation proposed by Abraham Maslow and Frederick Herzberg. This model is built on a basis of special non-continuous functions. This description may be a good basis for HR software and may be useful for business and management.