Off-lattice Monte Carlo simulations employing the PIVOT algorithm are used to generate ideal and excluded volume linear polymers in two dimensions. The form factor at small and large wave vectors is calculated from the resulting configurations and compared to the exact equation for ideal chains and to both scaling and renormalization group predictions for excluded volume chains. It is found that using the des Cloizeaux form for the distance distribution function in an analytic calculation of the form factor leads to close agreement with the Monte Carlo data and that simple expressions for both the small and large wave vector expansions reproduce the essential features of the form factor. (C) 2004 American Institute of Physics.