We introduce the concept of elastic reservation of bandwidth capacity to mitigate the problem of bandwidth fragmentation in LambdaGrids and present a network model which can support elastic reservations. We also define the Elastic Scheduling Problem (ESP), which succinctly captures the optimal utilization objective of elastic reservations. Analysis of ESP reveals that it is an NP-complete problem. Hence we present a heuristic algorithm, Squeeze In Stretch Out (SISO), for tackling ESP in polynomial time. SISO achieves good bandwidth utilization in simulation and efficiently handles the dynamic sharing of bandwidth between advance and immediate reservation requests. We also explore the impact of cost incentives for adopting elastic reservations on both the service provider and the user. In general, the approach for elastic reservation and scheduling presented in this paper is applicable to any concurrently accessible resource where the usage characteristics are quasi-flexible.