Substance is a philosophical term that seems to be often misunderstood (by non-professionals). In everyday language, "substance" is a mass term like "liquid". For example, there is a white substance in the flask or a white liquid in the flask. I've never seen a philosophical discussion of substances point out that in philosophy, "substance" is an individual term, not a mass term. It is like "entity" or "object", not like "liquid". The only way to figure this out is to pay careful attention to the examples of substances because the language is otherwise somewhat ambiguous.
In this question, I'm using the second definition of substance given in the SEP link: a substance is an object that is a basic entity. The important feature of a substance is that it has its own existence. It's existence is not derivative of anything else (although its continued existence may depend on the existence of other substances, for example, if a man is a substance, his continued existence depends on air).
There are just three different accounts of a physical object: it can be a substance, it can be an idea, or it can be a composite. This seems to cover all possibilities, as shown by the following analysis: an object either has its own existence or its existence is derivative of something else. If it has its own existence, then it is a substance. If its existence is derivative of something else, then that something else either involves mind or it does not. If the existence is derivative of something that involves mind, then it is an idea (I'm abbreviating all of the various forms of idealism by saying that the object is an idea, although it might be more complicated than that word suggests). If the object is not derivative of anything that involves mind, then its existence depends in some way on other objects. It could be composed of atoms or it could be essentially a part of a larger object or have some other essential relationship to other objects that makes it what it is. I'm abbreviating all such relationships by calling an object whose existence derives from such a relationship a composite.
If an object is composite, then the other objects on which its existence depends are also substance, idea, or composite. If you keep following this logic to its conclusion, then you ultimately come to a basis of physical existence that is either substance or idea. Note that it doesn't help to suggest a network of objects all of whose existence depends on each other with no final basis, because in that case, these objects would all be essential parts of a whole, which consisted of the aggregate of all of the objects.
I don't see any way around this. Either idealism or the old-fashioned idea of substances. And substances have some serious well-known philosophical problems such as how mind can be aware of them, and how they can interact.
Is this problem addressed in modern philosophy? If so, how?
ADDED: I was a little terse in my comments about "derivative of something else, so here is a bit more detail. One might claim that a car, for example doesn't have its own existence, that the existence of a car is based on its parts. It parts exist first, and then they are put together to make the car. The car is a composite of its parts. The existence of the car is derivative of its parts.
It can go the other way too. One might claim that individual physical things are all parts of the universe. It is the universe that exists, and the parts are just subdivisions of the universe; they don't have their own existence, but only as parts of a whole.
Both of the above examples have been been argued on both sides.