Simple problems are easy to model with the UML. Hard problems are easy to model, too, especially after you've become fluent in the language.
Reading about using the UML is one thing, but it's only through using the language that you will come to master it. Depending on your background, there are different ways to approach using the UML for the first time. As you gain more experience, you will come to understand and appreciate its more subtle parts.
If you can think it, the UML can model it.
You can model 80 percent of most problems by using about 20 percent of the UML. Basic structural things, such as classes, attributes, operations, use cases, ...