The polymer loop discussed in this paper was defined as a polymer chain

both ends of which are attached to a surface of impenetrated wall.In order to obtain the configurational statistics of this polymer loop

the exact enumeration and Monte Carlo methods were applied to the model of self-avoiding walk(SAW) on two- and three dimensional lattices.For the SAW on the simple cubic or square lattice

the maximum length of the model chain loop was 29 and 19

respectively.The numerical results based on the simulations were fitted to the scaling theory

by which the scaling exponents and other parameters were obtained and compared with the corresponding theoretala values.It was shown in the simulations that for these SAW loops the parallel components of their sizes with respect to the surface of the confined wall were larger than the perpendicular ones.It was interesting to notice that these results are contrary to those for the corresponding model tail chains

only one end of which is attached to the surface.