In this paper, we describe a computation platform called ReachLab, which enables automatic analysis of embedded software systems that interact with continuous environment. Algorithms are used to specify how the state space of the system model should be explored in order to perform analysis. In ReachLab, both system models and analysis algorithm models are specified in the same framework using Hybrid System Analysis and Design Language (HADL), which is a meta-model based language. The platform allows the models of algorithms to be constructed hierarchically and promotes their reuse in constructing more complex algorithms. Moreover, the platform is designed in such a way that the concerns of design and implementation of analysis algorithms are separated. On one hand, the models of analysis algorithms are abstract and therefore the design of algorithms can be made independent of implementation details. On the other hand, translators are provided to automatically generate implementations from the models for computing analysis results based on computation kernels. Multiple computation kernels, which are based on specific computation tools such as d/dt and the Level Set toolbox, are supported and can be chosen to enable hybrid state space exploration. An example is provided to illustrate the design and implementation process in ReachLab.