In this paper, we investigate homogeneous cylindrically symmetric Marder's universe in the presence of strange quark matter (SQM) source in f (R, T) gravity with cosmological constant Lambda. For this aim we have used the anisotropy feature (sigma(x)(x)/theta) of Marder type universe and equation of state (EoS) strange quark matter to obtain solutions in two classes f (R, T) gravity (Harko et al. in Phys. Rev. D 84:024020, 2011). Finally, some physical and kinematical properties are discussed.