The finite element (FE) method was used to investigate the failure of member connections of five glass fibre-reinforced polymer (GFRP) multiplanar truss bridges (MTB) with non-metallic connections. Three-dimensional FE models for the MTBs were developed and validated against previous experimental results and were accompanied by multiple parametric studies. Adhesive failure of the brace occurs progressively around the perimeter of the brace and GFRP laminate wrapping failure was not observed before adhesive bond failure of the brace. Furthermore, the failure sequence of the GFRP laminate layer and the adhesive bonding between the brace and chord was found to be dependent on the brace wall thickness. Extent of the predicted fibre tensile rupture of the GFRP laminate was greater for cement mortar grouted GFRP rods than its non-GFRP grouted counterpart.