When sending from Elastic Email, make sure you pick "Other" method in your MailPoet Settings>Send With tab:

This option will allow you to set up your custom SMTP connection. All the information can be found in your SMTP credentials:

server: smtp.elasticemail.com

port: 2525

username: your SMTP username

password: your SMTP username

Authentication: Yes

Secure Connection: TLS

Remember to check if your ports are open when trying to connect with MailPoet.

If you encounter connection issues, you should first try to connect to their server using another port (our default one is 2525 but this one may be blocked by your hosting company).
You can try to use the alternative SMTP configuration:

server: smtp25.elasticemail.com

port: 25

username: your SMTP username 

password: your SMTP username

Congratulations! You now have MailPoet configured with Elastic Email. MailPoet recommends you send 100 emails every 5 minutes if this is your first set up. You may increase it after a successful try.