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Rainfall in Bangladesh exhibits persistent wet and dry anomalies associated with occurrence of floods and droughts. Assessing inter-annual variability of rainfall is vital to account these hydrological extremes in the design and operations of water systems. However, the inter-annual variability obtained from short record rainfall data might be misleading as it does not contain whole climate variability which signifies the utmost importance of stochastic rainfall models. Since the inter-annual variability and stochastic models have not been explored adequately for rainfall in Bangladesh, this study evaluated (a) the spatio-temporal variability of rainfall focusing on inter-annual variability, and (b) applicability of a stochastic daily rainfall model, referred as the Decadal and Hierarchical Markov Chain (DHMC) model. Daily rainfall data of 1973-2012 for 18 stations across Bangladesh were used to investigate the probability distributions and autocorrelations of rainfall, and the model performances. Results show a higher magnitude of inter-annual variabilities of rainfall depth (standard deviation 80-250 mm) and wet spells (standard deviation 4-6 days) in wetter months (June to September) across rainfall stations in the east region of the country. In contrast, higher rates of inter-annual variabilities (i.e., coefficients of variations) were observed in drier months across the west region. Spatially, the dry spells were observed consistent across the country. Monthly rainfall showed decreasing trend over the region from west to the middle part of the country, whereas monthly number of wet days showed increasing trend over the eastern part. The DHMC was found to preserve the observed variabilities of rainfall at daily to multiyear resolutions at all stations, except a tendency to underestimate the autocorrelation of monthly rainfall depth. Despite this limitation, DHMC can be considered as a suitable stochastic rainfall simulator for a tropical monsoon climate like Bangladesh.