The emerging cloud computing and socially-enhanced services computing concepts offer several service models, including software-based and human-based services, for programming elastic composite applications utilizing human and software capabilities. However, the current view of elasticity still is centered on the elasticity of software resources. In this talk, we will systematically conceptualize principles for supporting multidimensional elasticity, covering resources (software and humans), quality (e.g., quality of service and quality of data), and costs and benefits (e.g., price, rewards and incentives). We then discuss enabling techniques for supporting multi-dimensional elasticity in data-, compute- and human-intensive processes. Finally, we will discuss some initial results and approaches on modeling multi-dimensional elasticity, programming software and human services, and elasticity reasoning.