Long-period vibrations felt by residents or workers in tall buildings due to wind or earthquake are a frequent problem. Considering the fact that vibration by wind or earthquake is dynamic, we investigated a wide range of random vibration, including long-period vibration. We focused on sensory evaluation and investigated the relationship between perception or psychological quantity (magnitude of anxiety or discomfort) and random vibration. In this study, we performed experiments using actual vibrations in detached houses for original waveforms. The results show the possibility of estimation using the predominant frequency in a fast Fourier transform analysis and maximum acceleration for perception and psychological evaluation. Random vibration is hardly perceived compared with sinusoidal vibration, and anxiety or discomfort is hardly felt. We determined a range in which subjects perceive random vibration but do not feel anxiety or discomfort.