Yes you can grow plants in shade.
It might seem impossible to grow plants in a shady garden, but providing some sunshine gets through and you select plants that are tolerant to the degree of shade in your garden, it is very possible.
These are the two things you need factor in to grow plants in shady gardens;
You might be surprised by the number of plants that will grow in shade, it is quite a long list.
Obviously in a garden with light shade the choice of plants will be greater, in deep shade choice will be limited. providing deep shade plants are positioned in the shadiest area and so on, most plants iI have listed can be used. I have listed a few more shade tolerant plants toward the bottom of this page.
If you like growing from seed, flowering annuals can be started indoors or in a greenhouse and then when big and sturdy enough, transplanted into the ground or containers.
A few more things to consider when growing in shade.
Other factors effecting planting in shady gardens are lack of moisture and nutrients.
*plants suitable for heavy shade; the rest need light or partial shade.