How to clone Python working environment on another machine?

Question

I developed a machine learning model with Python (Anaconda + Flask) on my workstation and all goes well. Later, I tried to ship this program onto another machine where of course I tried to set up the same environment, but the program fails to run. I copied the program to other machines where it also runs smoothly.

I cannot figure out what the problem is in the failed case (both the program code and the error message are copious so I am not able to present them here) but I'm almost certain that it is something with the different versions of the dependencies.

So, my question is that given an environment where a certain program runs well, how can I clone it to another where it should run well also? Of course, without the cloning of the full system ;)