The minimum perimeter polygon ( MPP) has been studied mostly within the image processing applications and computer processing of digitized contours. Among the pioneering articles certainly belongs one published by J. Sklanski and col. [1] and since then dozens of interesting approaches and algorithms were designed. It is worth of mentioning the works done by Slovak researchers Sloboda , Zaťko and Ferianc , too – see e.g. [2], [3] . I had taken a privilege to work with them for some time period almost three decades ago and they aroused the interest of the topic to me. However, the approach here is authentic and is based largely on the elastic fiber stretching simulation. Minimal Normed Built-In Circuits on the rectangular grid ( further MNBIC) take over the concept of MPP ( though not restricted to the closed curves and the clockwise rotation ). For the MNBIC we require that each vertex must be assigned to the vertex in grid and not beyond.