The glass-forming ability (GFA) of a number of the new multicomponent Fe-based alloys and their mechanical properties are investigated by X-ray diffractometry, differential scanning calorimetry, and microhardness measurements. The Fe$_{69}$Mn$_{1}$Mo$_{4}$Cr$_{2}$C$_{7}$P$_{10}$B$_{5}$Si$_{2}$ and Fe$_{55}$Ni$_{8}$Co$_{6}$Mo$_{4}$Cr$_{2}$V$_{1}$Al$_{2}$P$_{9}$C$_{6}$B$_{5}$Si$_{2}$ alloys are obtained in amorphous state by copper mould casting in plates with thickness of 0.5 and 2 mm, respectively, while crystallization of the Fe$_{50.0}$Ni$_{19.0}$Cr$_{6.5}$Мо$_{1.5}$V$_{1}$B$_{14.1}$С$_{2.5}$Р$_{4.4}$Si$_{1}$ alloy is suppressed only in thin ribbons produced by the melt-spinning processing. The GFA analysis is carried out in terms of the known thermodynamic criteria based on the values of temperatures of glass transition ($T_{g}$), onset crystallization ($T_{ons}$), and liquidus ($T_{l}$). As found, the critical cooling rates required for bulk amorphization of first two alloys predicted by the criterion of $\gamma_{m} = (2T_{ons} - T_{g})/T_{l}$ (1.01$\cdot$10$^{3}$ and 262 K/s, respectively) are in a good agreement with those (3150 и 303 K/s) estimated from the empirical ‘cooling rate—thickness’ relation. The investigated Fe-based bulk metallic glasses, whose chemical compositions may be formed using industrial raw materials, have a relatively high strength (up to 3.5 GPa) and are of interest from an application point of view.