AWS

ElastiCache

Cache Security Groups default group prevents access to cache cluster. In order to access cluster from an application, create a custom Cache Security Group, and authorize access for an appropriate EC2 security group (the one associated with the Elastic Beanstalk environment in question).

One (regularly very bad, but easy if you've just created an environment) way to find out which security group is used for the beanstalk environment is to scroll through its event logs back to when it was created. Name should be listed in one of the events.

A proper way to look up Beanstalk Security Group is to open CloudFormation AWS console, find the appropriate stack (see Description column), and check in the Resources tab.