Abstract: The endtoend vector distribution P(R) of a linear randomflight polymer chain with one end attached to an infinite large flat surface is investigated by Monte Carlo method.The meansquare endtoend distance can be given by =(4/3)n,and the mean angle by <θ>=45 ,where n is the chain length, θ is the angle between the endtoend vector R and Z axis normal to the surface.The radial distribution is P(R)dR=2A4 exp (－A2R2)R3 dR and the angular distribution isP(θ)dθ =sin 2θdθ ,here A2=3/(2n).The shape factor :: is about 1:2.73:12.5.The distribution of angle ,the angle between the longest principal axis L3 and Z axis,is approximately P(α)dα =sinαdα ,and its mean value <α> is nearly equal to 55.5 .

Key words: End-to-end vector, Shape factor, Distribution function, Polymer Chain excluded volume, real polymer chain