  In this work, we use McGuire's model to describe scattering of three spinless
identical particles in one spatial dimension, we first present analytic
solutions of Faddeev's equation for scattering of three spinless particles in
free space. The three particles interaction in finite volume is derived
subsequently, and the quantization conditions by matching wave functions in
free space and finite volume are presented in terms of two-body scattering
phase shifts. The quantization conditions obtained in this work for short range
interaction are L\"uscher's formula like and consistent with Yang's results in
\cite{Yang:1967bm}.
