Many elements in a web design influence the way a website publishes its content. This affects the spiders of the search engine such that they are unable to crawl within your website with ease. One cannot afford to ignore this fact and if you are concentrating on the on-page fundamentals of SEO, you will be fighting for visibility always.
Apart from this the content published on your website may have certain elements of the website design that can directly affect the SEO. A web design may be hard to understand, in case you are not familiar with its working, but plainly speaking it should be SEO-friendly.