Spectral line profiles of filaments/prominences to be observed by the Fast Imaging Solar Spectrograph (FISS) are studied. The main spectral lines of interests are $H{alpha}$, Ca II 8542, and Ca II K. FISS has a high spectral resolving power of $2{ imes}10^5$, and supports simultaneous dual-band recording. This instrument will be installed at the 1.6m New Solar Telescope (NST) of Big Bear Solar Observatory, which has a high spatial resolution of 0.065" at 500nm. Adopting the cloud model of radiative transfer and using the model parameters inferred from pre-existing observations, we have simulated a set of spectral profiles of the lines that are emitted by a filament on the disk or a prominence at the limb. Taking into account the parameters of the instrument, we have estimated the photon count to be recorded by the CCD cameras, the signal-to-noise ratios, and so on. We have also found that FISS is suitable for the study of multi-velocity threads in filaments if the spectral profiles of Ca II lines are recorded together with $H{alpha}$ lines.