Network function virtualization (NFV) allows service provides to implement network processing functionality in software using standard computing servers. As such, this approach precludes the need for deploying costly and proprietary hardware-based networking devices, i.e., black boxes, greatly reducing infrastructure and operational costs. Instead, operators can program and deploy desired network functions as software instances on commodity servers and further chain these functions to build end-user services, i.e., service function chaining (SFC). Although SFC mapping has received much focus in recent years, existing schemes assume that network functions are run in hypervisor-based virtual machines (VM). However VM-based strategies impose higher resource consumption at the server level and entail higher request processing/setup times. As a result, this paper analyzes container-based mapping approach which leverages VNF dependency relationships and incorporates resource constraints in the physical network. Performance results confirm that the proposed scheme gives notable gains versus VM hypervisor-based mapping, i.e., in terms of resource utilization, processing times and satisfied requests.