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The Anisimkin Jr. (AN) acoustic plate mode having dominant and depth-independent longitudinal displacement (u1 ≫ u2, u3; u1 ≈ constant) is numerically found in tetragonal 4mm Li2B4O7 crystal with one of the low-symmetry orientations (Euler angles 89°, 37°, 104°), as an example. The quasi-longitudinal (QL) modes with dominant and depth-dependent longitudinal displacement (u1 ≫ u2, u3; u1 ≠ constant) are experimentally detected along several propagation directions Θ in 128°y-LiNbO3 plate, where Θ = 0°, 30°, 60°, and 90° with respect to the x-axis. Compared with more symmetrical plate materials and orientations, the displacement profiles of the AN and QL modes in lower-symmetry counterparts are qualitatively the same, but their phase profiles are more complicated. Moreover, like any acoustic wave, all plate modes in anisotropic crystals suffer from beam steering, in general. The power flow angles of the modes propagating in a fixed direction are different and depend on the mode order n.