The phrase often signifies emotional reliance on others, highlighting a deep level of trust.

Emotional Support

Using 'rely upon' suggests that one can't manage without the help or support in question.

Not Independent

'Rely upon' can imply a sense of duty on the provider's part to not let the other down.

'Rely upon' used like this points to precise expectations one has from another.

There may be negative consequences if the trusted party fails to meet expectations.

In legal contexts, 'rely upon' conveys a strong belief in the evidence or argument.

It's used to describe the core support that legal arguments are built on.