Modest describes the personality trait or behaviour of not flaunting oneself, talking oneself up or putting oneself on display. Modest behaviour can be a response to compliments, praise or follow an achievement. Modesty can also manifested physically (for example, "dressing modestly", "modest accessories", "modest smile"). In contrast, "humble" refers specifically to a person's inner state and feelings. A humble person is willing to accept or respect another's authority, intellect and wisdom, or superiority without trying to challenge it or trying to assert oneself. In summary, being modest refers to your behaviour, being humble refers to your ego. (I found this meaning useful for your question )

Humble can only be use to describe personality, while modest can be use for physical appearance or objects as well.

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A humble person is willing to accept or respect another's authority, intellect and wisdom, or superiority without trying to challenge it or trying to assert oneself. In summary, being modest refers to your behaviour, being humble refers to your ego.