We present a first-principles lattice dynamics for the assembly of the transition-metal (M)-encapsulated Sin clusters in amorphous phase (a-MSin), which has been proposed as a potential candidate for the channel material of the next-generation thin-film transistors (TFTs) [N. Uchida et al., Appl. Phys. Express1, 121502 (2008)]. The shape of calculated vibrational density of states (VDOS) curve of a-MoSi10 is similar to the counterpart of the high pressure phase of a-Si (HPA-Si) although the present systems are obtained as a result of pressure relaxation. Its radial distribution function (RDF) among Si themselves is characterized by the absence of a gap between the first and second shells, which is also the case in . We further present the VDOS of a-WSi10, whose curve shape is again similar to that of HPA-Si. A difference between a-MoSi10 and a-WSi10 is that the W-atom displacement components extracted from the vibration eigenvectors are mainly distributed over a lower frequency range (< ~ 150 cm-1) than the Mo counterpart (~ 150 cm-1 to ~ 300 cm-1). This may be attributed to a larger atomic mass of W than Mo.