In this paper we will study equilibrium of one dimensional continuum. We will explain what continuum is and derive balance equation for elastic wire under tension, which is a second order linear differential equation. Additionally, we will derive equation of heat conduction through stick and show that this equation is identical to the balance equation of elastic wire. We will consider the behaviour of wire with respect to different boundary conditions. We will state and prove superposition principle which is very important for homogenzation of the boundary problem as well as for finding equilibrium position in general. At the end of this paper we will study uniqueness of the solution and go through cases when coefficients are not smooth enough. All mentioned results are complemented with a number of examples and illustrations.