In this note, two new very simple and computationally convenient external penalty functions are proposed for approximate solving of the linear programming problem with constraints-inequalities. The author calls these constructions  as composite ones. Both functions are a result of a smooth “gluing” of well-know quadratic penalty function with some barrier functions, namely inverse and logarithmic ones. As a result, the composite functions combine the positive properties both of their components. Similar to quadratic penalty function, the new constructions are defined overall space and demonstrate a stable work both inside and outside the feasible set of the original problem. At the same time, similar to barrier functions,  the composite functions make it possible to apply second-order methods for their minimization. The convergence theorems are proved, and encouraging results of numerical experiments are presented.