This paper describes a novel method to estimate sleep stage through noninvasive and unrestrained means. The Rechtschaffen and Kales (R-K) method is a standard to estimate sleep stage. However, it involves restraining the examinee and, thus, induces psychological stress. Furthermore, it requires specialists with a high degree of technical expertise and the use of an expensive polygraph. The sleep estimation method presented here is based on the noninvasive and unrestrained pneumatic biomeasurement method presented by the authors. Sleep stage transition in overnight sleep and the relationship between sleep stage and biosignals measured using the pneumatic method was analyzed and from the results, a mathematical model of sleep was created. Based on this model, a sleep stage estimator, including a sleep stage classifier and observer, was designed. The sleep state transition equation was the basis for the design of this observer, while the observed relationships were the basis for designing a classifier. Agreement of the estimated sleep stages with those obtained using the R-K method for the non-REM stage was 82.6%, for the REM stage was 38.3 % and for Wake was 70.5 %, including disagreement. However, the new method might ultimately result in better estimation of sleep stage due to the fact that it does not physically restrain the patient and does not induce psychological stress.