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Modelling vs. Modeling
As a verb, "model" refers to the job of a professional model, which is defined as wearing certain clothes for various shows, magazines or presentations. Nothing confusing until now. But at a closer look, you can easily spot that "model" is ending in the consonant + vowel + consonant pattern. In addition, it is also a two syllable word.
Such a situation often creates difficulties in deciding whether the rule of doubling the last consonant before adding the "-ing" suffix is or is not how you obtain the present participle or gerund form of the verb. And this is the cause that leads to the confusion people have when they have to decide whether "modelling" or "modeling" should be used.
 Modelling vs. Modeling
Well, just as it usually happens in this type of situations, where you can apply more rules to obtain a certain form of a word, both "modelling" and "modeling" are accepted as correct spellings that refer to the same action.
Even so, there are certain contexts in which you are required to use "modelling" and where you should use "modeling". More exactly, "modelling" is the UK spelling and "modeling" is the US spelling. You should pay attention to this fact when you are having a British/American English conversation, as the form you'll prefer will underline your knowledge of distinct spellings in the English vocabulary and your interest or consideration for the origin of your interlocutor.
When do we use "modelling"?
Given the fact that it ends in the consonant + vowel + consonant pattern, "model" is applying the rule that doubles the "l" before adding "-ing", to obtain its present participle form. This is how "modelling" is obtained, and this spelling is the most frequently used in English, especially in the UK.
When do we use "modeling"?
The American rules are slightly different for several English words, as they show more consideration for the ease of pronunciation. Consequently, there is a rule that claims that if a word has more than one syllable and the last syllable is not the stressed one, then the last letter should not be doubled before adding "-ing". This is how you get "modeling", which is a perfectly correct spelling according to this rule. You should be aware, anyway, that US is the only one that prefers this version and where it is often used.
Conclusion
Even if you say someone is "modelling" or "modeling", your message is the same. The main recommendation here, actually, is that you use "modelling" if you are communicating with a British English user and only use "modeling" if your interlocutor prefers the US spelling.