Fluid-solid phase transition and coexistence of square-well fluids confined in narrow cylindrical hard pores are characterized using molecular simulation methods. The equation of state containing a fluid phase, a solid phase and a fluid-solid coexistence state was separately obtained for different attractive ranges of potential well and pore diameters; lambda=1.2, 1.3, 1.4, and 1.5 for a pore of diameter D=2.2sigma, lambda=1.5 and 1.65 for a pore of diameter D=2.5sigma. For lambda=1.2, 1.3, and 1.4 at pore diameter D=2.2sigma, lambda=1.5 at D=2.5sigma, the fluid-solid phase coexistence densities and pressure are close to the hard sphere fluids at the same temperature, while the pressure decreases significantly for lambda=1.5 at D=2.2sigma and lambda=1.65 at D=2.5sigma, respectively. We also report the structural properties of the systems undergoing a phase transition.