Аннотация:In this chapter we consider the so-called pasture territory problem, its basic elements, and some related extremal problems. We describe the pasture territory as a graph of a piecewise smooth and continuous function f(x, y) defined on a closed, connected domain of a plane. Considering extremal problems is related with finding the location of the nomadic residence, when the exploiting pasture territory has maximum grass mass, and finding the bound of the territory, when the place of the residence is fixed [1, 2, 5].