The paper presents a systemic overview of constitutive models, i.e. mathematical or graphical representations of responses of a matter iniciated by its activation coming from its surroundings (especially stress- or strain-controlled loadings in mechanics). Various states of matter showing different behaviour are related with different distances among particles of the matter and their mutual movements. However, in oppostie to the previous centuries, when different approaches and methods were developed and used for description of various types of matters (in solid mechanics, hydromechanics, thermodynamics etc.), recently more and more often solid mechanics meets materials showing some features of fluids (e.g. creep, flow), and interactions of matters in different states (e.g. solid-liquid) need to be solved as well. The presented paper, together with another consequent one (Part II), creates a set of two related articles aiming at facilitating you the orientation in various types of constitutive equations. It presents graphical representations of basic mechanical resposnes (stress as a function of strain magnitude and strain rate, creep stress relaxation), as well as their simplified mathematical substantiation. Some more complex types of constitutive models will be presented in part II. On the base of these papers, the chapter on constitutive models was published in [1]. and Obsahuje seznam literatury