In this paper we carry out a study of modules over a 3 × 3 formal triangular matrix ring г=(T 0 0 M U 0 N○ u M N V ), where T, U, V are rings, M, N are U-T, V-U bimodules, respectively. Using the alternative description of left F-module as quintuple (A, B, C; f, g) with A E modT, B E modU and C ∈ modV, f : M T A → B ∈ modU, g : N u B → C ∈ modV, we shall characterize uniform, hollow and finitely embedded modules over F, respectively. Also the radical as well as the socle of г(A ○B○ C) is determined.
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