The engineering critical current density (J E ) and the index of transition, N (where E = αJ N ), of a Nb 3 Al multifilamentary strand, mass-produced as a part of the Fusion programme, have been characterized as a function of field (B), temperature (T ) and strain (ε) in the ranges B 15 T, 4.2 K T 16 K and −1.79% ε +0.67%. Complementary resistivity measurements were taken to determine the upper critical field (B C2 (T , ε)) and the critical temperature (T C (ε)) directly. The upper critical field defined at 5%ρ N , 50%ρ N or 95%ρ N , is described by the empirical relation B ρ N C2 (T , ε) = B ρ N C2 (0, ε) 1 − T T ρ N C (ε) ν . The upper critical field at zero 0953-2048/02/070991+20$30.00 © 2002 IOP Publishing Ltd Printed in the UK b 1 2where the Ginzburg-Landau (GL) parameter κ is given by the relation, γ is the Sommerfeld constant and t = T/T C (ε). At an applied field equal to the upper critical field found from fitting the Kramer dependence (i.e. at B C2 (T , ε)), the critical current is non-zero and we suggest that the current flow is percolative. The functional form of F P implies that in high fields the grain boundary pinning does not limit J E , this is consistent with J E -microstructure correlations in other superconducting materials.