We study through molecular dynamics finite element method with Stillinger-Weber potential the uniaxial compression of (0, 24) armchair and (31, 0) zigzag black phosphorene nanotubes with approximately equal diameters. Young's modulus, critical stress and critical strain are estimated with various tube lengths. It is found that under uniaxial compression the (0, 24) armchair black phosphorene nanotube buckles, whereas the failure of the (31, 0) zigzag one is caused by local bond breaking near the boundary.