We consider the statistical properties of dislocation line interacting with random array of point obstacles. They are essential to determine the plastic behavior of materials such as critical shear stress and dislocation velocity but they have not been obtained except small range of parameters. At first we have formulated a simulation algorithm, circle-rolling method analytically. This includes creating a transfer matrix between the 2 dislocation segments, solving the eigenvalue problem and evaluating the total transition probability for N-dislocation segments. The result shows that the distribution of an average characteristic angle <F> = 0 is simply given as N-fold convolution of individual distribution and change in the scale. Especially for large N, the asymptotic form of the distribution function can be obtained through the saddle point method. It turns out that segments tends to form quasi-straight line (<F> = 0) while they produce curve or loop pattern for small N. The other results useful to reduce the computation load are also reported.