Astrill VPN reports "Could not load SSL library" on login

First make sure you have openssl installed. You will need version 1.0 since Astrill does not support 1.1. To install 1.0.2, run

sudo apt install openssl=1.0.2g-1ubuntu4.8

Then install shared libraries, first check which version you want by running apt-cache search libssl | grep SSL. Example output:

libssl-dev - SSL development libraries, header files and documentation
libssl-doc - SSL development documentation documentation
libssl1.0.0 - SSL shared libraries  <-- version number

Install the library with the correct version:

sudo apt-get install libssl1.0.0

From the conversation in the comments, you also need to install libssl-dev, again, make sure the version is 1.0.

sudo apt install libssl-dev=1.0.2g-1ubuntu4.8

It is possible you need to install the packet ca-certificates as well.

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If the above did not solve the problem, open the file /etc/ld.so.conf as sudo and add a new line at the end

/usr/lib/x86_64-linux-gnu/openssl-1.0.0

Dependin on yuor system, the path could be different. Two other locations to try are /usr/local/lib and /usr/lib/openssl-1.0, see here and here.

Then run sudo ldconfig.

Following Hugh's comment on Shaido's answer, simply installing libssl-dev solved the problem.

sudo apt-get install libssl-dev