Collapse and fragmentation of primordial filamentary clouds under isotropic dissociation radiation is investigated with one-dimensional hydrodynamical calculations . We investigate the effect of dissociation photon on the filamentary clouds with calculating non-equilibrium chemical reactions . With the external radiation assumed to turn on when the filamentary cloud forms , the filamentary cloud with low initial density ( n _ { 0 } \leq 10 ^ { 2 } \mathrm { cm ^ { -3 } } ) suffers photodissociation of hydrogen molecules . In such a case , since main coolant is lost , temperature increases adiabatically enough to suppress collapse . As a result , the filamentary cloud fragments into very massive clouds ( \sim 10 ^ { 5 } M _ { \odot } ) . On the other hand , the evolution of the filamentary clouds with high initial density ( n _ { 0 } > 10 ^ { 2 } \mathrm { cm ^ { -3 } } ) is hardly affected by the external radiation . This is because the filamentary cloud with high initial density shields itself from the external radiation . It is found that the external radiation increases fragment mass . This result is consistent with previous results with one-zone models . It is also found that fragment mass decreases owing to the external dissociation radiation in the case with sufficiently large line mass .