For the use of screen printing, it’s a general rule that – design wise – boldness and simplicity work. You’re usually trying to convey a message quickly and clearly on your T shirt.
The same goes for most other forms of advertising – look at posters. People won’t usually spend time stopping and squinting. You have to hit them with interesting graphics/type – and usually just one or two main images.
Using few, bold, flat colours or monochrome design is a good way to go and has the added bonus of being easier and cheaper to print.
For inspiration, one great place to start looking is 2oth Century poster design. There are several ‘Ages’ to dip your toe into into, such as Art Deco, Constructivism, Futurism; as well as styles like comic book, jazz, film, theatre, tourism etc.

Take a look at this poster, Normandie (1935) by Adolphe Mouron Cassandre.
Monumental and minimal, you’ll never forget it. Cassandre was expert at conveying a message immediately. His posters for Dubonnet wine were amongst the first intended to be read by drivers passing by in fast moving cars. This kind of approach can look as good on a T shirt as on a poster.

Here’s another, similar example by Georges Dorival designed in 1928.

Here is a skyscraper drawing by Violette Engelberg. Hit them with that and they’ll feel it!

Very often, lettering is all you need. Typography is a powerful means of conveying mood as well as precise meaning.

El Lissitzky’s cover for the book The isms of Art (1925)

This is probably the most famous image created by the great Russian Constructivist Alexander Rodchenko.
It’s a lesson in the use of simple, striking type and dynamic blocks of flat colour which extend the calling motif in the photograph. It’s so good that it has been re-used in various forms umpteen times since.

Going back a little further, this is a billboard image advertising forthcoming productions in 1876 at a Glasgow theatre.
Such images were common in Victorian city streets. Note the use of various fonts to attract the eye to the details as well as the headlines. When treated with care, type-only designs can be rich in variety and strong in impact.

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Related posts:

1. Some favourite art and design sites
2. Designing for Screen printing and bling trainers
3. Index Separation Method for Screen Printing
4. Silk Screen Stencils
5. Text only T shirt designs